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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

(x-45)+(x-45)(3x-45)-540=0

We get rid of parentheses

x+(x-45)(3x-45)-45-540=0

We multiply parentheses ..

(+3x^2-45x-135x+2025)+x-45-540=0

We add all the numbers together, and all the variables

(+3x^2-45x-135x+2025)+x-585=0

We get rid of parentheses

3x^2-45x-135x+x+2025-585=0

We add all the numbers together, and all the variables

3x^2-179x+1440=0

a = 3; b = -179; c = +1440;
Δ = b2-4ac
Δ = -1792-4·3·1440
Δ = 14761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-179)-\sqrt{14761}}{2*3}=\frac{179-\sqrt{14761}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-179)+\sqrt{14761}}{2*3}=\frac{179+\sqrt{14761}}{6}
$