Quadratic equation calculator

Quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

2 * 90 = n * (n - 3) - n^{2} + 3 n + 180 = 0 n^{2} - 3 n - 180 = 0 a = 1; b = - 3; c = - 180 D = b^{2} - 4 a c = 3^{2} - 4 \cdot 1 \cdot (- 180) = 729 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{3 \pm 7 2 9}{2} n_{1, 2} = \frac{3 \pm 2 7}{2} n_{1, 2} = 1.5 \pm 13.5 n_{1} = 15 n_{2} = - 12 Factored form of the equation: (n - 15) (n + 12) = 0

Solution in text:

-n²+3n+180=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 729
D > 0 ... The equation has two distinct real roots

n₁ = 15
n₂ = -12

P = {15; -12}