(x+10)(600/x-5)=600

Solution for (x+10)(600/x-5)=600 equation:

(x+10)(600/x-5)=600

We move all terms to the left:

(x+10)(600/x-5)-(600)=0


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

x∈R


We multiply parentheses ..

(+600x^2-5x+6000x-50)-600=0

We get rid of parentheses

600x^2-5x+6000x-50-600=0

We add all the numbers together, and all the variables

600x^2+5995x-650=0

a = 600; b = 5995; c = -650;
Δ = b2-4ac
Δ = 59952-4·600·(-650)
Δ = 37500025
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:

$\sqrt{\Delta}=\sqrt{37500025}=\sqrt{25*1500001}=\sqrt{25}*\sqrt{1500001}=5\sqrt{1500001}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5995)-5\sqrt{1500001}}{2*600}=\frac{-5995-5\sqrt{1500001}}{1200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5995)+5\sqrt{1500001}}{2*600}=\frac{-5995+5\sqrt{1500001}}{1200}
$