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:

2 * (a + 4 + a) + 2 (a + 4) = a (a + 4) - a^{2} + 2 a + 16 = 0 a^{2} - 2 a - 16 = 0 p = 1; q = - 2; r = - 16 D = q^{2} - 4 p r = 2^{2} - 4 \cdot 1 \cdot (- 16) = 68 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{2 \pm 6 8}{2} = \frac{2 \pm 2 1 7}{2} a_{1, 2} = 1 \pm 4.123106 a_{1} = 5.123105626 a_{2} = - 3.123105626 Factored form of the equation: (a - 5.123105626) (a + 3.123105626) = 0

Solution in text:

-a²+2a+16=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 68
D > 0 ... The equation has two distinct real roots

a₁ = 5.1231056
a₂ = -3.1231056

P = {5.1231056; -3.1231056}