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:

a (a - 2) = 323 a^{2} - 2 a - 323 = 0 p = 1; q = - 2; r = - 323 D = q^{2} - 4 p r = 2^{2} - 4 \cdot 1 \cdot (- 323) = 1296 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{2 \pm 1 2 9 6}{2} a_{1, 2} = \frac{2 \pm 3 6}{2} a_{1, 2} = 1 \pm 18 a_{1} = 19 a_{2} = - 17 Factored form of the equation: (a - 19) (a + 17) = 0

Solution in text:

a²-2a-323=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1296
D > 0 ... The equation has two distinct real roots

a₁ = 19
a₂ = -17

P = {19; -17}