OceanCalc

Quadratic Formula Calculator

Solve quadratic equations of the form ax² + bx + c = 0 using the quadratic formula.

Enter Coefficients

For equation: ax² + bx + c = 0

The coefficient of x² (cannot be 0)

The coefficient of x

The constant term

The Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a

Discriminant (Δ = b² - 4ac):

  • Δ > 0: Two distinct real roots
  • Δ = 0: One repeated real root
  • Δ < 0: Two complex conjugate roots

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Solutions
x² - 5x + 6 = 0
Root x₁3
Root x₂2
Root TypeReal Roots
Discriminant (b² - 4ac)1
Vertex(2.5, -0.25)
Axis of Symmetryx = 2.5