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 + 2) * (a + 2) * (a + 2) - a * a * a = 728 6 a^{2} + 12 a - 720 = 0 6 = 2 \cdot 3 12 = 2^{2} \cdot 3 720 = 2^{4} \cdot 3^{2} \cdot 5 GCD (6, 12, 720) = 2 \cdot 3 = 6 a^{2} + 2 a - 120 = 0 p = 1; q = 2; r = - 120 D = q^{2} - 4 p r = 2^{2} - 4 \cdot 1 \cdot (- 120) = 484 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{- 2 \pm 4 8 4}{2} a_{1, 2} = \frac{- 2 \pm 2 2}{2} a_{1, 2} = - 1 \pm 11 a_{1} = 10 a_{2} = - 12 Factored form of the equation: (a - 10) (a + 12) = 0

Solution in text:

6a²+12a-720=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 17424
D > 0 ... The equation has two distinct real roots

a₁ = 10
a₂ = -12

P = {10; -12}