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:

12 x^{2} - 7 x - 12 = 0 12 x^{2} - 7 x - 12 = 0 a = 12; b = - 7; c = - 12 D = b^{2} - 4 a c = 7^{2} - 4 \cdot 12 \cdot (- 12) = 625 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{7 \pm 6 2 5}{2 4} x_{1, 2} = \frac{7 \pm 2 5}{2 4} x_{1, 2} = 0.291667 \pm 1.041667 x_{1} = 1.333333333 x_{2} = - 0.75 Factored form of the equation: 12 (x - 1.333333333) (x + 0.75) = 0

Solution in text:

12x²-7x-12=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 625
D > 0 ... The equation has two distinct real roots

x₁ = 1.3333333
x₂ = -0.75

P = {1.3333333; -0.75}