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:

7 * (x - 10) + 7 * x = (x - 10) * x - x^{2} + 24 x - 70 = 0 x^{2} - 24 x + 70 = 0 a = 1; b = - 24; c = 70 D = b^{2} - 4 a c = 2 4^{2} - 4 \cdot 1 \cdot 70 = 296 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 4 \pm 2 9 6}{2} = \frac{2 4 \pm 2 7 4}{2} x_{1, 2} = 12 \pm 8.602325 x_{1} = 20.602325267 x_{2} = 3.397674733 Factored form of the equation: (x - 20.602325267) (x - 3.397674733) = 0

Solution in text:

-x²+24x-70=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 296
D > 0 ... The equation has two distinct real roots

x₁ = 20.6023253
x₂ = 3.3976747

P = {20.6023253; 3.3976747}