(600/x+5)(x-4)=600

Solution for (600/x+5)(x-4)=600 equation:

(600/x+5)(x-4)=600

We move all terms to the left:

(600/x+5)(x-4)-(600)=0


Domain of the equation: x+5)(x-4)!=0

x∈R


We multiply parentheses ..

(+600x^2-2400x+5x-20)-600=0

We get rid of parentheses

600x^2-2400x+5x-20-600=0

We add all the numbers together, and all the variables

600x^2-2395x-620=0

a = 600; b = -2395; c = -620;
Δ = b2-4ac
Δ = -23952-4·600·(-620)
Δ = 7224025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7224025}=\sqrt{25*288961}=\sqrt{25}*\sqrt{288961}=5\sqrt{288961}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2395)-5\sqrt{288961}}{2*600}=\frac{2395-5\sqrt{288961}}{1200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2395)+5\sqrt{288961}}{2*600}=\frac{2395+5\sqrt{288961}}{1200}
$