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:

8 * 7 = (n + 2) (n + 1) - n^{2} - 3 n + 54 = 0 n^{2} + 3 n - 54 = 0 a = 1; b = 3; c = - 54 D = b^{2} - 4 a c = 3^{2} - 4 \cdot 1 \cdot (- 54) = 225 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 3 \pm 2 2 5}{2} n_{1, 2} = \frac{- 3 \pm 1 5}{2} n_{1, 2} = - 1.5 \pm 7.5 n_{1} = 6 n_{2} = - 9 Factored form of the equation: (n - 6) (n + 9) = 0

Solution in text:

-n²-3n+54=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 225
D > 0 ... The equation has two distinct real roots

n₁ = 6
n₂ = -9

P = {6; -9}