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:

96 = a * (a + 4) - a^{2} - 4 a + 96 = 0 a^{2} + 4 a - 96 = 0 p = 1; q = 4; r = - 96 D = q^{2} - 4 p r = 4^{2} - 4 \cdot 1 \cdot (- 96) = 400 D > 0 a_{1, 2} = \frac{- q \pm D}{2 p} = \frac{- 4 \pm 4 0 0}{2} a_{1, 2} = \frac{- 4 \pm 2 0}{2} a_{1, 2} = - 2 \pm 10 a_{1} = 8 a_{2} = - 12 Factored form of the equation: (a - 8) (a + 12) = 0

Solution in text:

-a²-4a+96=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 400
D > 0 ... The equation has two distinct real roots

a₁ = 8
a₂ = -12

P = {8; -12}