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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

(+X^2-30X-30X+900)+2X-570=0

We get rid of parentheses

X^2-30X-30X+2X+900-570=0

We add all the numbers together, and all the variables

X^2-58X+330=0

a = 1; b = -58; c = +330;
Δ = b2-4ac
Δ = -582-4·1·330
Δ = 2044
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:

$\sqrt{\Delta}=\sqrt{2044}=\sqrt{4*511}=\sqrt{4}*\sqrt{511}=2\sqrt{511}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-58)-2\sqrt{511}}{2*1}=\frac{58-2\sqrt{511}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-58)+2\sqrt{511}}{2*1}=\frac{58+2\sqrt{511}}{2}
$