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:

(3 + 0.40 b) * b = 135 0.40000000000001 b^{2} + 3 b - 135 = 0 p = 0.4; q = 3; r = - 135 D = q^{2} - 4 p r = 3^{2} - 4 \cdot 0.4 \cdot (- 135) = 225 D > 0 b_{1, 2} = \frac{- q \pm D}{2 p} = \frac{- 3 \pm 2 2 5}{0 . 8} b_{1, 2} = - 3.75 \pm 18.75 b_{1} = 15 b_{2} = - 22.5 Factored form of the equation: 0.40000000000001 (b - 15) (b + 22.5) = 0

Solution in text:

0.40000000000001b²+3b-135=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 225
D > 0 ... The equation has two distinct real roots

b₁ = 15
b₂ = -22.5

P = {15; -22.5}