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 (11 - a) = 30 - a^{2} + 11 a - 30 = 0 a^{2} - 11 a + 30 = 0 p = 1; q = - 11; r = 30 D = q^{2} - 4 p r = 1 1^{2} - 4 \cdot 1 \cdot 30 = 1 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 1 \pm 1}{2} a_{1, 2} = \frac{1 1 \pm 1}{2} a_{1, 2} = 5.5 \pm 0.5 a_{1} = 6 a_{2} = 5 Factored form of the equation: (a - 6) (a - 5) = 0

Solution in text:

-a²+11a-30=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1
D > 0 ... The equation has two distinct real roots

a₁ = 6
a₂ = 5

P = {6; 5}