(2x-4)(2x-4)+(2x-4)=30

Solution for (2x-4)(2x-4)+(2x-4)=30 equation:

(2x-4)(2x-4)+(2x-4)=30

We move all terms to the left:

(2x-4)(2x-4)+(2x-4)-(30)=0

We get rid of parentheses

(2x-4)(2x-4)+2x-4-30=0

We multiply parentheses ..

(+4x^2-8x-8x+16)+2x-4-30=0

We add all the numbers together, and all the variables

(+4x^2-8x-8x+16)+2x-34=0

We get rid of parentheses

4x^2-8x-8x+2x+16-34=0

We add all the numbers together, and all the variables

4x^2-14x-18=0

a = 4; b = -14; c = -18;
Δ = b2-4ac
Δ = -142-4·4·(-18)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-22}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+22}{2*4}=\frac{36}{8}
=4+1/2
$