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:

2 x^{2} + 3 x - 9 = 0 2 x^{2} + 3 x - 9 = 0 a = 2; b = 3; c = - 9 D = b^{2} - 4 a c = 3^{2} - 4 \cdot 2 \cdot (- 9) = 81 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 3 \pm 8 1}{4} x_{1, 2} = \frac{- 3 \pm 9}{4} x_{1, 2} = - 0.75 \pm 2.25 x_{1} = 1.5 x_{2} = - 3 Factored form of the equation: 2 (x - 1.5) (x + 3) = 0

Solution in text:

2x²+3x-9=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 81
D > 0 ... The equation has two distinct real roots

x₁ = 1.5
x₂ = -3

P = {1.5; -3}