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^{2} - 6 + 10 a = 4 / 8 a a^{2} + 9.5 a - 6 = 0 p = 1; q = 9.5; r = - 6 D = q^{2} - 4 p r = 9 . 5^{2} - 4 \cdot 1 \cdot (- 6) = 114.25 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{- 9 . 5 \pm 1 1 4 . 2 5}{2} a_{1, 2} = - 4.75 \pm 5.34439 a_{1} = 0.594389582 a_{2} = - 10.094389582 Factored form of the equation: (a - 0.594389582) (a + 10.094389582) = 0

Solution in text:

a²+9.5a-6=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 114.25
D > 0 ... The equation has two distinct real roots

a₁ = 0.5943896
a₂ = -10.0943896

P = {0.5943896; -10.0943896}