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:

6 = a (6 - a) a^{2} - 6 a + 6 = 0 p = 1; q = - 6; r = 6 D = q^{2} - 4 p r = 6^{2} - 4 \cdot 1 \cdot 6 = 12 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{6 \pm 1 2}{2} = \frac{6 \pm 2 3}{2} a_{1, 2} = 3 \pm 1.732051 a_{1} = 4.732050808 a_{2} = 1.267949192 Factored form of the equation: (a - 4.732050808) (a - 1.267949192) = 0

Solution in text:

a²-6a+6=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 12
D > 0 ... The equation has two distinct real roots

a₁ = 4.7320508
a₂ = 1.2679492

P = {4.7320508; 1.2679492}