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:

10 = 15 * x - 0.5 * 9.81 * x^{2} 4.905 x^{2} - 15 x + 10 = 0 a = 4.905; b = - 15; c = 10 D = b^{2} - 4 a c = 1 5^{2} - 4 \cdot 4.905 \cdot 10 = 28.8 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{1 5 \pm 2 8 . 8}{9 . 8 1} x_{1, 2} = 1.529052 \pm 0.54705 x_{1} = 2.076102257 x_{2} = 0.982001718 Factored form of the equation: 4.905 (x - 2.076102257) (x - 0.982001718) = 0

Solution in text:

4.905x²-15x+10=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 28.8
D > 0 ... The equation has two distinct real roots

x₁ = 2.0761023
x₂ = 0.9820017

P = {2.0761023; 0.9820017}