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:

200 = n * (17 + n) - n^{2} - 17 n + 200 = 0 n^{2} + 17 n - 200 = 0 a = 1; b = 17; c = - 200 D = b^{2} - 4 a c = 1 7^{2} - 4 \cdot 1 \cdot (- 200) = 1089 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 7 \pm 1 0 8 9}{2} n_{1, 2} = \frac{- 1 7 \pm 3 3}{2} n_{1, 2} = - 8.5 \pm 16.5 n_{1} = 8 n_{2} = - 25 Factored form of the equation: (n - 8) (n + 25) = 0

Solution in text:

-n²-17n+200=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1089
D > 0 ... The equation has two distinct real roots

n₁ = 8
n₂ = -25

P = {8; -25}