Equation Solver — Quadratic & Linear System
Solve quadratics (real/complex roots + discriminant) and 2×2 linear systems. Client-side.
How to use
- 1 Quadratic: enter a, b and c for ax² + bx + c = 0.
- 2 Linear system: enter the coefficients of two equations in x and y.
- 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 = 0Output
x = 3, x = 2 (discriminant = 1)Common use cases
-
1
Algebra homework
Solve quadratics and check the discriminant.
-
2
Systems of equations
Find x and y for a pair of linear equations.
-
3
Physics & geometry
Solve quadratics arising from motion or area problems.
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
- Quadratic Equation — Wolfram MathWorld — Wolfram MathWorld
- Quadratic formula — Wikipedia
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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