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 * 96 - 8 n^{2} - 16 n = 0 - 8 n^{2} - 16 n + 192 = 0 8 n^{2} + 16 n - 192 = 0 8 = 2^{3} 16 = 2^{4} 192 = 2^{6} \cdot 3 GCD (8, 16, 192) = 2^{3} = 8 n^{2} + 2 n - 24 = 0 a = 1; b = 2; c = - 24 D = b^{2} - 4 a c = 2^{2} - 4 \cdot 1 \cdot (- 24) = 100 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 2 \pm 1 0 0}{2} n_{1, 2} = \frac{- 2 \pm 1 0}{2} n_{1, 2} = - 1 \pm 5 n_{1} = 4 n_{2} = - 6 Factored form of the equation: (n - 4) (n + 6) = 0

Solution in text:

-8n²-16n+192=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 6400
D > 0 ... The equation has two distinct real roots

n₁ = 4
n₂ = -6

P = {4; -6}