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 * (- 1560) = n * (2 * (- 56) - (- 1) * (n - 1)) - n^{2} + 113 n - 3120 = 0 n^{2} - 113 n + 3120 = 0 a = 1; b = - 113; c = 3120 D = b^{2} - 4 a c = 11 3^{2} - 4 \cdot 1 \cdot 3120 = 289 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 1 3 \pm 2 8 9}{2} n_{1, 2} = \frac{1 1 3 \pm 1 7}{2} n_{1, 2} = 56.5 \pm 8.5 n_{1} = 65 n_{2} = 48 Factored form of the equation: (n - 65) (n - 48) = 0

Solution in text:

-n²+113n-3120=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 289
D > 0 ... The equation has two distinct real roots

n₁ = 65
n₂ = 48

P = {65; 48}