Calculyn

Quadratic Formula Calculator

Solve ax² + bx + c = 0 and see the roots, discriminant and vertex.

Results update as you type.

Two real roots

1discriminant

x = 2 or x = 1

Vertex x
1.5
Vertex y
-0.25
Two real roots1

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How it works

The discriminant (b² − 4ac) tells you how many real solutions there are: positive means two, zero means one, negative means two complex roots.

Formula

x = (−b ± √(b² − 4ac)) ÷ 2a

Example

x² − 3x + 2 = 0: discriminant = 1, so x = 2 or x = 1.

Assumptions & limitations

  • Results are rounded for display.

Frequently asked questions

What's the vertex?

The highest or lowest point of the parabola y = ax² + bx + c.