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:

(1 + b) * b = 4 b^{2} + b - 4 = 0 p = 1; q = 1; r = - 4 D = q^{2} - 4 p r = 1^{2} - 4 \cdot 1 \cdot (- 4) = 17 D > 0 b_{1, 2} = \frac{- q \pm D}{2 p} = \frac{- 1 \pm 1 7}{2} b_{1, 2} = - 0.5 \pm 2.061553 b_{1} = 1.561552813 b_{2} = - 2.561552813 Factored form of the equation: (b - 1.561552813) (b + 2.561552813) = 0

Solution in text:

b²+b-4=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 17
D > 0 ... The equation has two distinct real roots

b₁ = 1.5615528
b₂ = -2.5615528

P = {1.5615528; -2.5615528}