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:

b^{2} - b - 20 = 0 b^{2} - b - 20 = 0 p = 1; q = - 1; r = - 20 D = q^{2} - 4 p r = 1^{2} - 4 \cdot 1 \cdot (- 20) = 81 D > 0 b_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 \pm 8 1}{2} b_{1, 2} = \frac{1 \pm 9}{2} b_{1, 2} = 0.5 \pm 4.5 b_{1} = 5 b_{2} = - 4 Factored form of the equation: (b - 5) (b + 4) = 0

Solution in text:

b²-b-20=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 81
D > 0 ... The equation has two distinct real roots

b₁ = 5
b₂ = -4

P = {5; -4}