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:

n (n - 1) = 3 * (n - 4) * (n - 5) - 2 n^{2} + 26 n - 60 = 0 2 n^{2} - 26 n + 60 = 0 2 . . . prime number 26 = 2 \cdot 13 60 = 2^{2} \cdot 3 \cdot 5 GCD (2, 26, 60) = 2 = 2 n^{2} - 13 n + 30 = 0 a = 1; b = - 13; c = 30 D = b^{2} - 4 a c = 1 3^{2} - 4 \cdot 1 \cdot 30 = 49 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 3 \pm 4 9}{2} n_{1, 2} = \frac{1 3 \pm 7}{2} n_{1, 2} = 6.5 \pm 3.5 n_{1} = 10 n_{2} = 3 Factored form of the equation: (n - 10) (n - 3) = 0

Solution in text:

-2n²+26n-60=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 196
D > 0 ... The equation has two distinct real roots

n₁ = 10
n₂ = 3

P = {10; 3}