MATH · FREE ONLINE CALCULATOR

X Pro Super Solver Calculator

A free-form equation solver for polynomials, fractions, brackets, roots, logarithms, exponents, trigonometry and linear systems. It expands, rearranges and solves automatically, checks every answer and graphs the result.

Detailed optionsStep-by-step guideWorked examples

01 / ONE BOX. ANY EQUATION.

What would you like to solve?

Polynomials, fractions, brackets, roots, logarithms, exponents, trigonometry and linear systems. Separate several equations with commas.

Try:

02 / YOUR ANSWER

2 real solutions

Read as: x² − 5x + 6 = 0

Read the equationx² − 5x + 6 = 0
Move every term to one sidex² − 5x + 6 = 0
Simplify to standard formx² − 5x + 6 = 0
Use the quadratic formulaΔ = b² − 4ac = 1 · x = (−b ± √Δ) ÷ 2a
Check the solutionsx = 2: 0 = 0 · x = 3: 0 = 0

Solving for xx = 2 x = 3

Standard form: x² − 5x + 6 = 0

Where the graph meets zeroMove across the graph to read values

YOUR ANIMATED GUIDE

Replay the solution, step by step.

These steps use your current inputs. Choose a step or play the walkthrough.

STEP 1 / 5

Solve for x

12345

Read the equation

The solver reads implicit multiplication (2x, 3(x+1)) and the usual order of operations.

x² − 5x + 6 = 0

Explore at your own pace

How to use this x pro super solver calculator

The X Pro Super Solver is a free-form equation solver. Type an equation the way you would write it on paper, with brackets, fractions, powers, roots, logarithms, exponentials or trigonometry, and it chooses the right method automatically. Polynomial and rational equations are expanded and solved completely, including complex roots. Other equations are solved numerically and checked by substitution. You can also enter several linear equations separated by commas.

How the solver reads your equation

The input is parsed with the usual order of operations: brackets, powers, multiplication and division, then addition and subtraction. Implicit multiplication works, so 2x, 3(x + 1) and (x + 1)(x − 1) are understood. Use ^ for powers, sqrt( ) for square roots, |x| for absolute value, and π or e for the constants. If no equals sign is typed, the solver finds where the expression equals zero; if there is no unknown at all, it simply evaluates the expression.

Exact methods for polynomial and rational equations

When both sides are polynomials or fractions of polynomials, the solver multiplies through by the denominators, expands everything and collects like terms into standard form. Linear equations are isolated directly, quadratics use the discriminant and quadratic formula, and higher degrees combine the rational root test with a numerical method that finds all complex roots at once. Every candidate is substituted into the original equation, and values that would make a denominator zero are rejected as extraneous.

Numerical methods for everything else

Equations with roots, logarithms, exponentials or trigonometric functions generally have no algebraic formula. The solver samples f(x) = left side − right side 24,000 times across the search range, finds sign changes and touching points, then narrows each one by bisection. Jumps across vertical asymptotes are discarded. For periodic trigonometric equations it detects the period and reports a general solution such as x = π/6 + 2π·k.

X Pro Super Solver formulas, explained

One side equals zero

f(x) = left side − right side = 0

Every equation in one unknown is rewritten this way before it is solved.

Quadratic step

x = (−b ± √(b² − 4ac)) ÷ 2a

Used whenever the standard form has degree 2.

Bisection

If f(a) and f(b) have opposite signs, a root lies between them. Halve the interval until it is tiny.

Reliable for continuous functions; each halving adds about one binary digit of accuracy.

General trigonometric solution

x = x₀ + P·k, k = 0, ±1, ±2, …

P is the detected period, x₀ each base solution in [0, P).

PUT THE FORMULA TO WORK

Worked examples you can try.

Load an example into the calculator, then change one value to explore.

EXAMPLE 01

Brackets on both sides

3(x − 2) + 4 = 2x² − 5 simplifies to −2x² + 3x + 3 = 0, giving x = (3 ± √33)/4.

EXAMPLE 02

An extraneous root

x/(x − 2) = 2/(x − 2) leads to x = 2, but that makes the denominator zero, so the equation has no solution.

EXAMPLE 03

A square-root equation

√(x + 3) = x − 3 has the single solution x = 6. Squaring would also produce x = 1, which fails the check.

EXAMPLE 04

A trigonometric equation

sin(x) = 0.5 has the general solution x = π/6 + 2πk and x = 5π/6 + 2πk.

EXAMPLE 05

A system of equations

x + y = 10 and x − y = 2 are solved together: x = 6 and y = 4.

MAKE THE NUMBERS MAKE SENSE

Common mistakes to avoid

Writing 1/2x when you mean 1/(2x). Without brackets it is read as (1/2)·x.
Typing sin(30) in radians mode when you mean 30 degrees. Switch angles to degrees in Options.
Expecting every solution of a periodic equation inside a narrow search range. Use the general solution or widen the range.

A LITTLE MORE CLARITY

Frequently asked questions

How do I type an equation?

Type it as you would write it, for example 3(x − 2) + 4 = 2x² − 5. Use ^ for powers, sqrt( ) for square roots and commas to separate equations in a system.

Does the super solver show its working?

Yes. Each answer comes with the rearranged standard form, the method used, a substitution check and an animated step-by-step guide.

What can the X Pro Super Solver solve?

Linear, quadratic, cubic and higher polynomial equations, equations with fractions, absolute values, square and cube roots, logarithms, exponentials and trigonometric functions, plus systems of up to four linear equations. Expressions without an unknown are evaluated like a scientific calculator.

Why are some answers exact and others decimal?

Exact forms such as 7/3, 2√2 or π/6 are shown when the solver can confirm them. Equations that need a numerical search have decimal answers accurate to about 15 significant digits, rounded for display.

What does “rejected” mean?

Multiplying by a denominator can introduce values that do not satisfy the original equation because they make a denominator zero. The solver checks every candidate and lists those it rejected.

Which functions and symbols are supported?

+ − × ÷ ^, brackets, |x|, sqrt, cbrt, ln, log (base 10), log2, exp, sin, cos, tan, sec, csc, cot, asin, acos, atan, sinh, cosh, tanh, π and e. You can type × and ÷ or * and /, and superscripts such as x² are understood.

Is my equation sent anywhere?

No. Solving happens entirely in your browser. Recently solved equations are kept only in this browser’s local storage, and you can clear them at any time.

Methodology & assumptions

Calculations run in your browser using the formulas and assumptions explained on this page. Intermediate values retain full floating-point precision; displayed amounts are rounded. Undefined operations such as division by zero are rejected, every candidate solution is substituted back into the original equation, and numerical answers are refined to about 15 significant digits. Sharing an input link places those inputs in the URL.

Further reading:Durand–Kerner method for polynomial roots Bisection method