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Equation Solver — Quadratic & Linear System

Solve quadratics (real/complex roots + discriminant) and 2×2 linear systems. Client-side.

Free No signup Client-side Privacy friendly Updated
x² + x + = 0
x + y =
x + y =

How to use

  1. 1 Quadratic: enter a, b and c for ax² + bx + c = 0.
  2. 2 Linear system: enter the coefficients of two equations in x and y.
  3. 3 Roots (real or complex) and the discriminant are shown instantly.

Why use this tool

  • Solve quadratics with real or complex roots, plus the discriminant.
  • Solve a 2×2 system of linear equations with Cramer’s rule.
  • Runs entirely in your browser.

Frequently asked questions

What is the quadratic formula?

x = (−b ± √(b² − 4ac)) / 2a. The part under the root, b² − 4ac, is the discriminant.

What does the discriminant tell me?

If it’s positive there are two real roots; if zero, one repeated real root; if negative, two complex-conjugate roots.

How is the linear system solved?

By Cramer’s rule using determinants. If the determinant of the coefficient matrix is zero, there is no unique solution.

Does it handle a = 0?

Yes — it falls back to solving the linear equation bx + c = 0.

What is Equation Solver?

An equation solver finds the roots of a quadratic equation ax²+bx+c=0 — including complex roots and the discriminant — and solves a 2×2 system of linear equations using Cramer’s rule.

Features

Quadratic & linear

Solve ax² + bx + c = 0 and 2×2 systems of linear equations.

Discriminant & root type

Shows the discriminant and whether there are two, one, or no real roots.

Free & private

Runs on your device — nothing is uploaded.

Example

Input

x² − 5x + 6 = 0

Output

x = 3, x = 2  (discriminant = 1)

Common use cases

  1. 1

    Algebra homework

    Solve quadratics and check the discriminant.

  2. 2

    Systems of equations

    Find x and y for a pair of linear equations.

  3. 3

    Physics & geometry

    Solve quadratics arising from motion or area problems.

Summary

Zerethon's equation solver finds the roots of quadratic equations ax² + bx + c = 0 (reporting the discriminant and real roots) and solves 2×2 linear systems, in your browser. Everything runs client-side — nothing is uploaded.

Category
Math
Pricing
Free
Privacy
Browser-based
Signup
Not required

References

Privacy

Your data never leaves your browser unless explicitly stated. Equation Solver runs entirely client-side — no server upload, no logging, no tracking of your input.

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