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Quadratic Formula Calculator

Solve quadratic equations ax²+bx+c=0 using the quadratic formula with step-by-step solutions

100% FreeStep-by-Step Solutions

Enter coefficients for the equation ax² + bx + c = 0

Coefficient a (x² term)

Coefficient b (x term)

Coefficient c (constant term)

Try These Examples

Click on any example to automatically fill the calculator

Example 1

x² - 5x + 6 = 0

a: 1

b: -5

c: 6

Example 2

2x² + 3x - 2 = 0

a: 2

b: 3

c: -2

Example 3

x² - 4x + 4 = 0 (perfect square)

a: 1

b: -4

c: 4

Example 4

x² + 2x + 5 = 0 (complex roots)

a: 1

b: 2

c: 5

Quadratic Formula

The quadratic formula solves equations of the form ax² + bx + c = 0:

x = \\frac{-b \\pm \\sqrt{b^2 - 4ac}}{2a}

The expression under the square root (b² - 4ac) is called the discriminant.

Discriminant Analysis

Δ > 0: Two distinct real roots

Δ = 0: One repeated real root (perfect square)

Δ < 0: Two complex conjugate roots

\\Delta = b^2 - 4ac