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) = 3080 n^{2} - n - 3080 = 0 a = 1; b = - 1; c = - 3080 D = b^{2} - 4 a c = 1^{2} - 4 \cdot 1 \cdot (- 3080) = 12321 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 \pm 1 2 3 2 1}{2} n_{1, 2} = \frac{1 \pm 1 1 1}{2} n_{1, 2} = 0.5 \pm 55.5 n_{1} = 56 n_{2} = - 55 Factored form of the equation: (n - 56) (n + 55) = 0

Solution in text:

n²-n-3080=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 12321
D > 0 ... The equation has two distinct real roots

n₁ = 56
n₂ = -55

P = {56; -55}