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 - 5) + 9 * x = (x - 5) * x - x^{2} + 23 x - 45 = 0 x^{2} - 23 x + 45 = 0 a = 1; b = - 23; c = 45 D = b^{2} - 4 a c = 2 3^{2} - 4 \cdot 1 \cdot 45 = 349 D > 0 x_{1, 2} = \frac{- b \pm D}{2 a} = \frac{2 3 \pm 3 4 9}{2} x_{1, 2} = 11.5 \pm 9.340771 x_{1} = 20.840770846 x_{2} = 2.159229154 Factored form of the equation: (x - 20.840770846) (x - 2.159229154) = 0

Solution in text:

-x²+23x-45=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 349
D > 0 ... The equation has two distinct real roots

x₁ = 20.8407708
x₂ = 2.1592292

P = {20.8407708; 2.1592292}