Quadratic equation solver

Solve ax² + bx + c = 0 for real or complex roots, with the discriminant and vertex shown.

1x² − 3x + 2 = 0

Rootsx₁ = 2, x₂ = 1

Discriminant (b² − 4ac)1

Vertex(1.5, -0.25)

Frequently asked questions

What formula is used?

The quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a.

What does the discriminant tell me?

Positive means two real roots, zero means one repeated root, and negative means two complex roots.

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Quadratic equation solver

Solve ax² + bx + c = 0 for real or complex roots, with the discriminant and vertex shown.

1x² − 3x + 2 = 0

Rootsx₁ = 2, x₂ = 1

Discriminant (b² − 4ac)1

Vertex(1.5, -0.25)

Frequently asked questions

What formula is used?

The quadratic formula x = (−b ± √(b² − 4ac)) ÷ 2a.

What does the discriminant tell me?

Positive means two real roots, zero means one repeated root, and negative means two complex roots.

Related tools

See all 7 free math tools

Scientific Calculator

Trig, logs, powers, roots and factorials with a full keypad.

Use Scientific Calculator

Ohm's Law Calculator

Find voltage, current, resistance or power from any two values.

Use Ohm's Law Calculator

Resistor Color Code

Read 4- and 5-band resistor values and tolerance from their colours.

Use Resistor Color Code

Statistics Calculator

Mean, median, mode, range, variance and standard deviation.

Use Statistics Calculator