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:

4 * 3 * 2 * 3 = (n - 2) (n - 3) - n^{2} + 5 n + 66 = 0 n^{2} - 5 n - 66 = 0 a = 1; b = - 5; c = - 66 D = b^{2} - 4 a c = 5^{2} - 4 \cdot 1 \cdot (- 66) = 289 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{5 \pm 2 8 9}{2} n_{1, 2} = \frac{5 \pm 1 7}{2} n_{1, 2} = 2.5 \pm 8.5 n_{1} = 11 n_{2} = - 6 Factored form of the equation: (n - 11) (n + 6) = 0

Solution in text:

-n²+5n+66=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 289
D > 0 ... The equation has two distinct real roots

n₁ = 11
n₂ = -6

P = {11; -6}