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:

6 * ((a + 5) + a) = (a + 5) * a - a^{2} + 7 a + 30 = 0 a^{2} - 7 a - 30 = 0 p = 1; q = - 7; r = - 30 D = q^{2} - 4 p r = 7^{2} - 4 \cdot 1 \cdot (- 30) = 169 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{7 \pm 1 6 9}{2} a_{1, 2} = \frac{7 \pm 1 3}{2} a_{1, 2} = 3.5 \pm 6.5 a_{1} = 10 a_{2} = - 3 Factored form of the equation: (a - 10) (a + 3) = 0

Solution in text:

-a²+7a+30=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 169
D > 0 ... The equation has two distinct real roots

a₁ = 10
a₂ = -3

P = {10; -3}