Equation Solver

Type your equation's numbers and get every root, with the working and a graph.

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Equation Solver

Linear, quadratic, polynomial and systems, with working

Quadratic: ax² + bx + c = 0

a (x² coefficient)

b (x coefficient)

c (constant)

Rootsx₁ = 2, x₂ = 3

Vertex(2.5, -0.25)turning point of the curve

Real roots2

Complex roots0

How it works

A root of an equation is a value that makes it true. Linear equations have one root, a quadratic has up to two, and a polynomial of degree n has n roots when complex ones are counted. A system finds values that satisfy every equation at once.

Equation: 1x² + -5x + 6 = 0
Discriminant D = b² − 4ac = -5² − 4 × 1 × 6 = 1
D > 0, so there are two different real roots.
x = (−b ± √D) ÷ 2a = (5 ± 1) ÷ 2
x₁ = 2, x₂ = 3

Put 0 for any missing power, for example x³ − 4 is 1, 0, 0, -4.
The discriminant D = b² − 4ac tells you the kind of quadratic roots before you solve.
For a system, lines that meet once have one solution, parallel lines none, and the same line infinitely many.

Linear: x = (c − b) ÷ a. Quadratic: x = (−b ± √D) ÷ 2a, using the numerically stable form so tiny roots keep full precision. Polynomials: zero roots stripped, rational root theorem for integers, then Aberth iteration with Newton polishing in double precision. Systems: the determinant and Cramer's rule, with Gaussian elimination and partial pivoting to detect no or infinitely many solutions.

Preparing tool

How to use Equation Solver

Choose the type: linear, quadratic, polynomial or a system of equations.
Enter the numbers in front of each term (the coefficients).
Read the roots, follow the working, and check the graph where the curve crosses zero.

Read the detailed guide →

What are the limits of Equation Solver?

You enter coefficients rather than typing a free-form equation. Polynomials up to degree 10 are solved numerically in double precision (about 12 correct digits; very close repeated roots may show slight rounding). Systems must be 2×2 or 3×3. Nothing you enter leaves your device.