(x-6)(540/x-6)=540

Solution for (x-6)(540/x-6)=540 equation:

(x-6)(540/x-6)=540

We move all terms to the left:

(x-6)(540/x-6)-(540)=0


Domain of the equation: x-6)!=0

x∈R


We multiply parentheses ..

(+540x^2-6x-3240x+36)-540=0

We get rid of parentheses

540x^2-6x-3240x+36-540=0

We add all the numbers together, and all the variables

540x^2-3246x-504=0

a = 540; b = -3246; c = -504;
Δ = b2-4ac
Δ = -32462-4·540·(-504)
Δ = 11625156
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:

$\sqrt{\Delta}=\sqrt{11625156}=\sqrt{36*322921}=\sqrt{36}*\sqrt{322921}=6\sqrt{322921}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3246)-6\sqrt{322921}}{2*540}=\frac{3246-6\sqrt{322921}}{1080}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3246)+6\sqrt{322921}}{2*540}=\frac{3246+6\sqrt{322921}}{1080}
$