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:

(2 b - 3)^{2} + b^{2} = 233 5 b^{2} - 12 b - 224 = 0 p = 5; q = - 12; r = - 224 D = q^{2} - 4 p r = 1 2^{2} - 4 \cdot 5 \cdot (- 224) = 4624 D > 0 b_{1, 2} = \frac{- q \pm D}{2 p} = \frac{1 2 \pm 4 6 2 4}{1 0} b_{1, 2} = \frac{1 2 \pm 6 8}{1 0} b_{1, 2} = 1.2 \pm 6.8 b_{1} = 8 b_{2} = - 5.6 Factored form of the equation: 5 (b - 8) (b + 5.6) = 0

Solution in text:

5b²-12b-224=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 4624
D > 0 ... The equation has two distinct real roots

b₁ = 8
b₂ = -5.6

P = {8; -5.6}