Equation Solver — Linear, Quadratic and Simultaneous Equations

Solve linear, quadratic and higher-degree equations in x, or systems of two or three linear equations, with exact answers and worked steps.

Free, with no sign-up and no watermark. The file is processed in your browser and never uploaded.

Type an equation in x — such as 3x + 5 = 20, x^2 - 5x + 6 = 0 or 2(x - 1) = x + 4 — and get the solution with steps. Quadratics show the discriminant and exact roots with simplified square roots (including complex roots); cubic and higher equations are solved numerically. You can also solve systems of two or three linear equations exactly.

Step by step

  1. Choose the type: Pick Equation in x or System of equations.
  2. Enter the equation: Use ^ for powers (x^2), and brackets freely. Click an example to start from it.
  3. For a system: Choose 2 (x, y) or 3 (x, y, z) and fill each coefficient and right-hand side — fractions are allowed.
  4. Read the solution: Roots or values appear at the top, exact forms underneath, then the steps or row operations.

Handy for

Quadratics

Get roots like (5 ± √13)/2 exactly, plus decimals.

Simultaneous equations

Solve 2x + 3y = 13 and x − y = −1 with Gauss–Jordan steps.

Rearranged equations

Equations with x on both sides or in brackets are expanded automatically.

Checking higher-degree work

Find all roots of a cubic or quartic numerically.

Good to know

  • Equations with x in a denominator are allowed: any root that makes the original equation undefined is rejected and explained.

  • Functions like sin(x) = 0 aren’t polynomials, so they can’t be solved here — plot them in the Graphing Calculator instead.

  • Systems tell you when there is no solution (parallel) or infinitely many (dependent equations).

Questions

How accurate are cubic and higher roots?

They are found numerically and are accurate to about 12 significant digits. Linear and quadratic answers with rational coefficients are exact.

Can I use variables other than x?

Equations must use x. Systems use x, y and z.

Is anything uploaded?

No. Everything runs in your browser, and anything you save (decks, timetables, results) stays in this browser’s local storage on your device.

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