Quadratic equation calculator

Quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

a (a + 6) / 2 = 216 0.5 a^{2} + 3 a - 216 = 0 p = 0.5; q = 3; r = - 216 D = q^{2} - 4 p r = 3^{2} - 4 \cdot 0.5 \cdot (- 216) = 441 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{- 3 \pm 4 4 1}{1} = - 3 \pm 211 a_{1, 2} = - 3 \pm 21 a_{1} = 18 a_{2} = - 24 Factored form of the equation: 0.5 (a - 18) (a + 24) = 0

Solution in text:

0.5a²+3a-216=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 441
D > 0 ... The equation has two distinct real roots

a₁ = 18
a₂ = -24

P = {18; -24}