(x-30)+x+(x-30)(x-30)+x=540

Solution for (x-30)+x+(x-30)(x-30)+x=540 equation:

(x-30)+x+(x-30)(x-30)+x=540

We move all terms to the left:

(x-30)+x+(x-30)(x-30)+x-(540)=0

We add all the numbers together, and all the variables

2x+(x-30)+(x-30)(x-30)-540=0

We get rid of parentheses

2x+x+(x-30)(x-30)-30-540=0

We multiply parentheses ..

(+x^2-30x-30x+900)+2x+x-30-540=0

We add all the numbers together, and all the variables

(+x^2-30x-30x+900)+3x-570=0

We get rid of parentheses

x^2-30x-30x+3x+900-570=0

We add all the numbers together, and all the variables

x^2-57x+330=0

a = 1; b = -57; c = +330;
Δ = b2-4ac
Δ = -572-4·1·330
Δ = 1929
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{-(-57)-\sqrt{1929}}{2*1}=\frac{57-\sqrt{1929}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+\sqrt{1929}}{2*1}=\frac{57+\sqrt{1929}}{2}
$