Equation Solver
Solve linear, quadratic, cubic and higher equations with exact roots and steps.
Type The Equation, Get Every Root
Write the equation the way it appears on the page — 2x^2 - 3x = 5, 3(x + 1) = 2x - 4 or (x - 1)(x + 2) = 0 — and the solver expands both sides, gathers every term on one side and finds each value of x that makes it true.
Linear and quadratic equations come with the full working: the rearranged form, the discriminant, and roots written exactly as fractions or surds such as (3 ± √49)/4 as well as decimals. Cubic and higher polynomials, up to degree eight, are solved numerically to twelve significant figures, complex roots included.
Key features
- Natural input — brackets, implied multiplication and powers are expanded for you.
- Exact answers — fractions and simplified square roots, not just decimals.
- Step-by-step working for linear and quadratic equations.
- Degrees up to eight, with real and complex roots.
- Private — nothing you type leaves your browser.
This tool runs entirely inside your browser using native Web APIs. Your files and text are never uploaded to a server, never logged and never shared with third parties.
How to use: Equation Solver
- Type the equation
Use ^ for powers. Anything on the right of = is moved across for you. - Read the standard form
Check the rearranged polynomial matches what you meant. - See the roots
Exact form first, then the decimal value of each root. - Follow the working
For quadratics, the discriminant tells you how many real roots to expect.
Technical specifications
| Processing location | Entirely in your browser — no server round trip |
|---|---|
| Data uploaded | None. Files and text never leave your device |
| Price | Free — no account, no trial, no usage cap |
| Category | Calculators |
| Works offline | Yes, once the page has loaded |
| Browser support | Chrome 90+, Edge 90+, Firefox 90+, Safari 15+ |
| Interface languages | English, 中文, हिन्दी, Español, العربية |
Frequently asked questions
How do I solve a quadratic equation?
Rearrange it to ax² + bx + c = 0 and use the quadratic formula x = (−b ± √(b² − 4ac)) / 2a. The solver does exactly that and shows each step: the discriminant b² − 4ac is positive for two real roots, zero for one repeated root and negative for two complex roots.
Can it solve cubic and quartic equations?
Yes. Any polynomial up to degree eight is solved numerically with the Durand–Kerner method, which finds all roots at once — real and complex — accurate to about twelve significant figures.
Why does it say division by x is not supported?
Dividing by an expression containing x turns the equation into a rational one that can gain or lose solutions. Multiply both sides by the denominator first, then solve the polynomial that results — and check the answers do not make the original denominator zero.
What does a complex root mean?
It means the graph of the polynomial never crosses the x-axis at that point. Complex roots of equations with real coefficients always come in pairs like 1 + 2i and 1 − 2i.
Can it solve systems of equations?
Not here — this solves one equation in one unknown. For a system of linear equations, use the Matrix Calculator’s Solve operation, which works in exact fractions.