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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-89x-585=0

a = 2; b = -89; c = -585;
Δ = b2-4ac
Δ = -892-4·2·(-585)
Δ = 12601
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{-(-89)-\sqrt{12601}}{2*2}=\frac{89-\sqrt{12601}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89)+\sqrt{12601}}{2*2}=\frac{89+\sqrt{12601}}{4}
$