Equation solver

Solve linear and quadratic equations and systems of two equations with two unknowns.

How it works

A quadratic equation ax² + bx + c = 0 has two solutions, one repeated solution or no real ones, depending on the discriminant Δ = b² − 4ac being positive, zero or negative. When it’s negative, the solutions are complex numbers.

Systems of two equations are solved here with Cramer’s rule.

x = (−b ± √(b² − 4ac)) / 2a

Frequently asked questions

What if a is 0?

Then it isn’t quadratic but linear: bx + c = 0, with solution x = −c/b.

What is the vertex of the parabola?

The highest or lowest point of y = ax² + bx + c. It’s at x = −b / 2a.

When does a system have no solution?

When the two lines are parallel: the determinant is 0 and the equations aren’t equivalent.

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