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:

n * (n - 1) = 20 n^{2} - n - 20 = 0 a = 1; b = - 1; c = - 20 D = b^{2} - 4 a c = 1^{2} - 4 \cdot 1 \cdot (- 20) = 81 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 \pm 8 1}{2} n_{1, 2} = \frac{1 \pm 9}{2} n_{1, 2} = 0.5 \pm 4.5 n_{1} = 5 n_{2} = - 4 Factored form of the equation: (n - 5) (n + 4) = 0

Solution in text:

n²-n-20=0 ... quadratic equation

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

n₁ = 5
n₂ = -4

P = {5; -4}