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:

- 4 x^{2} + 5 x = 0 - 4 x^{2} + 5 x = 0 4 x^{2} - 5 x = 0 a = 4; b = - 5; c = 0 D = b^{2} - 4 a c = 5^{2} - 4 \cdot 4 \cdot 0 = 25 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{5 \pm 2 5}{8} x_{1, 2} = \frac{5 \pm 5}{8} x_{1, 2} = 0.625 \pm 0.625 x_{1} = 1.25 x_{2} = 0 Factored form of the equation: 4 (x - 1.25) x = 0

Solution in text:

-4x²+5x=0 ... c=0; quadratic equation without constant term

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

x₁ = 1.25
x₂ = 0

P = {1.25; 0}