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:

153 = a * (2 * a - 1) - 2 a^{2} + a + 153 = 0 2 a^{2} - a - 153 = 0 p = 2; q = - 1; r = - 153 D = q^{2} - 4 p r = 1^{2} - 4 \cdot 2 \cdot (- 153) = 1225 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 \pm 1 2 2 5}{4} a_{1, 2} = \frac{1 \pm 3 5}{4} a_{1, 2} = 0.25 \pm 8.75 a_{1} = 9 a_{2} = - 8.5 Factored form of the equation: 2 (a - 9) (a + 8.5) = 0

Solution in text:

-2a²+a+153=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 1225
D > 0 ... The equation has two distinct real roots

a₁ = 9
a₂ = -8.5

P = {9; -8.5}