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:

50 = 2 * n + n * (n - 1) / 2 - 0.5 n^{2} - 1.5 n + 50 = 0 0.5 n^{2} + 1.5 n - 50 = 0 a = 0.5; b = 1.5; c = - 50 D = b^{2} - 4 a c = 1 . 5^{2} - 4 \cdot 0.5 \cdot (- 50) = 102.25 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 1 . 5 \pm 1 0 2 . 2 5}{1} n_{1, 2} = - 1.5 \pm 10.111874 n_{1} = 8.611874208 n_{2} = - 11.611874208 Factored form of the equation: 0.5 (n - 8.611874208) (n + 11.611874208) = 0

Solution in text:

-0.5n²-1.5n+50=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 102.25
D > 0 ... The equation has two distinct real roots

n₁ = 8.6118742
n₂ = -11.6118742

P = {8.6118742; -11.6118742}