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

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

(X-30)(X-30)+X(X-30)+X+X=540

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

X^2+2X+(X-30)(X-30)-30X-540=0

We multiply parentheses ..

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

We add all the numbers together, and all the variables

X^2+(+X^2-30X-30X+900)-28X-540=0

We get rid of parentheses

X^2+X^2-30X-30X-28X+900-540=0

We add all the numbers together, and all the variables

2X^2-88X+360=0

a = 2; b = -88; c = +360;
Δ = b2-4ac
Δ = -882-4·2·360
Δ = 4864
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:

$\sqrt{\Delta}=\sqrt{4864}=\sqrt{256*19}=\sqrt{256}*\sqrt{19}=16\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-16\sqrt{19}}{2*2}=\frac{88-16\sqrt{19}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+16\sqrt{19}}{2*2}=\frac{88+16\sqrt{19}}{4}
$