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:

4 * 20000 * n = 20000 * n^{2} - 4 * 480000 - 20000 n^{2} + 80000 n + 1920000 = 0 20000 n^{2} - 80000 n - 1920000 = 0 20000 = 2^{5} \cdot 5^{4} 80000 = 2^{7} \cdot 5^{4} 1920000 = 2^{10} \cdot 3 \cdot 5^{4} GCD (20000, 80000, 1920000) = 2^{5} \cdot 5^{4} = 20000 n^{2} - 4 n - 96 = 0 a = 1; b = - 4; c = - 96 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 1 \cdot (- 96) = 400 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 \pm 4 0 0}{2} n_{1, 2} = \frac{4 \pm 2 0}{2} n_{1, 2} = 2 \pm 10 n_{1} = 12 n_{2} = - 8 Factored form of the equation: (n - 12) (n + 8) = 0

Solution in text:

-20000n²+80000n+1920000=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 160000000000
D > 0 ... The equation has two distinct real roots

n₁ = 12
n₂ = -8

P = {12; -8}