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:

(9 x - 4) * (3 x - 2) = 8 + 5 x 27 x^{2} - 35 x = 0 a = 27; b = - 35; c = 0 D = b^{2} - 4 a c = 3 5^{2} - 4 \cdot 27 \cdot 0 = 1225 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{3 5 \pm 1 2 2 5}{5 4} x_{1, 2} = \frac{3 5 \pm 3 5}{5 4} x_{1, 2} = 0.648148 \pm 0.648148 x_{1} = 1.296296296 x_{2} = 0 Factored form of the equation: 27 (x - 1.296296296) x = 0

Solution in text:

27x²-35x=0 ... c=0; quadratic equation without constant term

Discriminant:
D = b² - 4ac = 1225
D > 0 ... The equation has two distinct real roots

x₁ = 1.2962963
x₂ = 0

P = {1.2962963; 0}