(x-40)*(600/x+3)=540

Solution for (x-40)*(600/x+3)=540 equation:

(x-40)(600/x+3)=540

We move all terms to the left:

(x-40)(600/x+3)-(540)=0


Domain of the equation: x+3)!=0

x∈R


We multiply parentheses ..

(+600x^2+3x-24000x-120)-540=0

We get rid of parentheses

600x^2+3x-24000x-120-540=0

We add all the numbers together, and all the variables

600x^2-23997x-660=0

a = 600; b = -23997; c = -660;
Δ = b2-4ac
Δ = -239972-4·600·(-660)
Δ = 577440009
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:

$\sqrt{\Delta}=\sqrt{577440009}=\sqrt{81*7128889}=\sqrt{81}*\sqrt{7128889}=9\sqrt{7128889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23997)-9\sqrt{7128889}}{2*600}=\frac{23997-9\sqrt{7128889}}{1200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23997)+9\sqrt{7128889}}{2*600}=\frac{23997+9\sqrt{7128889}}{1200}
$