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:

400 - 5 * x^{2} - 10 x = 0 - 5 x^{2} - 10 x + 400 = 0 5 x^{2} + 10 x - 400 = 0 5 . . . prime number 10 = 2 \cdot 5 400 = 2^{4} \cdot 5^{2} GCD (5, 10, 400) = 5 = 5 x^{2} + 2 x - 80 = 0 a = 1; b = 2; c = - 80 D = b^{2} - 4 a c = 2^{2} - 4 \cdot 1 \cdot (- 80) = 324 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{- 2 \pm 3 2 4}{2} x_{1, 2} = \frac{- 2 \pm 1 8}{2} x_{1, 2} = - 1 \pm 9 x_{1} = 8 x_{2} = - 10 Factored form of the equation: (x - 8) (x + 10) = 0

Solution in text:

-5x²-10x+400=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 8100
D > 0 ... The equation has two distinct real roots

x₁ = 8
x₂ = -10

P = {8; -10}