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} = x + 3 2 x^{2} - x - 3 = 0 a = 2; b = - 1; c = - 3 D = b^{2} - 4 a c = 1^{2} - 4 \cdot 2 \cdot (- 3) = 25 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 \pm 2 5}{4} x_{1, 2} = \frac{1 \pm 5}{4} x_{1, 2} = 0.25 \pm 1.25 x_{1} = 1.5 x_{2} = - 1 Factored form of the equation: 2 (x - 1.5) (x + 1) = 0

Solution in text:

2x²-x-3=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 25
D > 0 ... The equation has two distinct real roots

x₁ = 1.5
x₂ = -1

P = {1.5; -1}