(x-45)+x+x(x-45)+(x-45)=540

Solution for (x-45)+x+x(x-45)+(x-45)=540 equation:

(x-45)+x+x(x-45)+(x-45)=540

We move all terms to the left:

(x-45)+x+x(x-45)+(x-45)-(540)=0

We add all the numbers together, and all the variables

x+(x-45)+x(x-45)+(x-45)-540=0

We multiply parentheses

x^2+x+(x-45)-45x+(x-45)-540=0

We get rid of parentheses

x^2+x+x-45x+x-45-45-540=0

We add all the numbers together, and all the variables

x^2-42x-630=0

a = 1; b = -42; c = -630;
Δ = b2-4ac
Δ = -422-4·1·(-630)
Δ = 4284
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:

$\sqrt{\Delta}=\sqrt{4284}=\sqrt{36*119}=\sqrt{36}*\sqrt{119}=6\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{119}}{2*1}=\frac{42-6\sqrt{119}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{119}}{2*1}=\frac{42+6\sqrt{119}}{2}
$