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 - 6 = 0 4 x^{2} + 5 x - 6 = 0 a = 4; b = 5; c = - 6 D = b^{2} - 4 a c = 5^{2} - 4 \cdot 4 \cdot (- 6) = 121 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 5 \pm 1 2 1}{8} x_{1, 2} = \frac{- 5 \pm 1 1}{8} x_{1, 2} = - 0.625 \pm 1.375 x_{1} = 0.75 x_{2} = - 2 Factored form of the equation: 4 (x - 0.75) (x + 2) = 0

Solution in text:

4x²+5x-6=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 121
D > 0 ... The equation has two distinct real roots

x₁ = 0.75
x₂ = -2

P = {0.75; -2}