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:

3000 = b * (b + 10) - b^{2} - 10 b + 3000 = 0 b^{2} + 10 b - 3000 = 0 p = 1; q = 10; r = - 3000 D = q^{2} - 4 p r = 1 0^{2} - 4 \cdot 1 \cdot (- 3000) = 12100 D > 0 b_{1, 2} = \frac{- q \pm D}{2 p} = \frac{- 1 0 \pm 1 2 1 0 0}{2} b_{1, 2} = \frac{- 1 0 \pm 1 1 0}{2} b_{1, 2} = - 5 \pm 55 b_{1} = 50 b_{2} = - 60 Factored form of the equation: (b - 50) (b + 60) = 0

Solution in text:

-b²-10b+3000=0 ... quadratic equation

Discriminant:
D = b² - 4ac = 12100
D > 0 ... The equation has two distinct real roots

b₁ = 50
b₂ = -60

P = {50; -60}