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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2-59X+330=0

a = 1; b = -59; c = +330;
Δ = b2-4ac
Δ = -592-4·1·330
Δ = 2161
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{-(-59)-\sqrt{2161}}{2*1}=\frac{59-\sqrt{2161}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+\sqrt{2161}}{2*1}=\frac{59+\sqrt{2161}}{2}
$