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:

3 * 2 = (n - 2) (n - 3) - n^{2} + 5 n = 0 n^{2} - 5 n = 0 a = 1; b = - 5; c = 0 D = b^{2} - 4 a c = 5^{2} - 4 \cdot 1 \cdot 0 = 25 D > 0 n_{1, 2} = \frac{- b \pm D}{2 a} = \frac{5 \pm 2 5}{2} n_{1, 2} = \frac{5 \pm 5}{2} n_{1, 2} = 2.5 \pm 2.5 n_{1} = 5 n_{2} = 0 Factored form of the equation: (n - 5) n = 0

Solution in text:

-n²+5n=0 ... c=0; quadratic equation without constant term

Discriminant:
D = b² - 4ac = 25
D > 0 ... The equation has two distinct real roots

n₁ = 5
n₂ = 0

P = {5; 0}