Quadratic Equation Calculator

A quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the coefficients a, b, and c of the quadratic equation in its basic standardized form. The solution of a quadratic equation usually consists of two distinct real or complex roots, or one double root — calculated using the discriminant.

Calculation:

3 / 2 - (2 x - 1)^{2} = 5 / 4 - 4 x^{2} + 4 x - 0.75 = 0 4 x^{2} - 4 x + 0.75 = 0 a = 4; b = - 4; c = 0.75 D = b^{2} - 4 a c = 4^{2} - 4 \cdot 4 \cdot 0.75 = 4 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 \pm 4}{8} x_{1, 2} = \frac{4 \pm 2}{8} x_{1, 2} = 0.5 \pm 0.25 x_{1} = 0.75 x_{2} = 0.25 Factored form of the equation: 4 (x - 0.75) (x - 0.25) = 0

Solution in text:

-4x²+4x-0.75=0 ... quadratic equation

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

x₁ = 0.75
x₂ = 0.25

P = {0.75; 0.25}