Quadratic Equation Calculator

A quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

x^{2} - x - 12 = 0 a = 1; b = - 1; c = - 12 D = b^{2} - 4 a c = 1^{2} - 4 \cdot 1 \cdot (- 12) = 49 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 \pm 4 9}{2} x_{1, 2} = \frac{1 \pm 7}{2} x_{1, 2} = 0.5 \pm 3.5 x_{1} = 4 x_{2} = - 3 Factored form of the equation: (x - 4) (x + 3) = 0

Solution in text:

x²-x-12=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 49
D > 0 ... The equation has two distinct real roots

x₁ = 4
x₂ = -3

P = {4; -3}