Quadratic Equation Calculator

Solve any quadratic equation ax² + bx + c = 0 and see the steps, vertex and graph.

Negative numbers and fractions work.
Solutions
Roots
Discriminant
Vertex
Factored form
Sum and product of roots
Work

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The Quadratic Formula

x = (−b ± √(b² − 4ac)) ÷ 2a

The discriminant b² − 4ac tells you the kind of roots: positive gives two real roots, zero gives one repeated root, negative gives two complex roots. The vertex of the parabola is at x = −b ÷ 2a.

Worked Example

Tips

Check your answer by plugging a root back in: 5² − 3(5) − 10 = 0. The roots add up to −b/a and multiply to c/a.