Quadratic Formula Calculator

Solve any quadratic equation in the form ax² + bx + c = 0. Simply enter the coefficients 'a', 'b', and 'c', and the calculator will determine the roots of the equation, including complex (imaginary) solutions.

Enter Coefficients

Solution

(1)x² + (5)x + (6) = 0
Discriminant (Δ)1
Nature of RootsTwo distinct real roots
Root x₁ -2
Root x₂ -3

The Quadratic Formula

The roots of a quadratic equation are found using the formula:

x = (-b ± √(b² - 4ac)) / 2a

The value inside the square root, Δ = b² - 4ac, is called the discriminant. It determines the nature of the roots:

  • If Δ > 0, there are two distinct real roots.
  • If Δ = 0, there is exactly one real root.
  • If Δ < 0, there are two complex (imaginary) roots.