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) / 2 = 105 0.5 n^{2} - 0.5 n - 105 = 0 a = 0.5; b = - 0.5; c = - 105 D = b^{2} - 4 a c = 0 . 5^{2} - 4 \cdot 0.5 \cdot (- 105) = 210.25 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{0 . 5 \pm 2 1 0 . 2 5}{1} n_{1, 2} = 0.5 \pm 14.5 n_{1} = 15 n_{2} = - 14 Factored form of the equation: 0.5 (n - 15) (n + 14) = 0

Solution in text:

0.5n²-0.5n-105=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 210.25
D > 0 ... The equation has two distinct real roots

n₁ = 15
n₂ = -14

P = {15; -14}