Quadratic equation calculator

Quadratic equation has the basic form:

a x^{2} + b x + c = 0

Enter the quadratic equation's coefficients a, b, and c of its basic standardized form. A solution of quadratic equations is usually two different real or complex roots or one double root — the calculation using the discriminant.

Calculation:

x (42 - x) = 1 8^{2} - x^{2} + 42 x - 324 = 0 x^{2} - 42 x + 324 = 0 a = 1; b = - 42; c = 324 D = b^{2} - 4 a c = 4 2^{2} - 4 \cdot 1 \cdot 324 = 468 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{4 2 \pm 4 6 8}{2} = \frac{4 2 \pm 6 1 3}{2} x_{1, 2} = 21 \pm 10.816654 x_{1} = 31.816653826 x_{2} = 10.183346174 Factored form of the equation: (x - 31.816653826) (x - 10.183346174) = 0

Solution in text:

-x²+42x-324=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 468
D > 0 ... The equation has two distinct real roots

x₁ = 31.8166538
x₂ = 10.1833462

P = {31.8166538; 10.1833462}