(2x-8)(2x-8)=55

Solution for (2x-8)(2x-8)=55 equation:

(2x-8)(2x-8)=55

We move all terms to the left:

(2x-8)(2x-8)-(55)=0

We multiply parentheses ..

(+4x^2-16x-16x+64)-55=0

We get rid of parentheses

4x^2-16x-16x+64-55=0

We add all the numbers together, and all the variables

4x^2-32x+9=0

a = 4; b = -32; c = +9;
Δ = b2-4ac
Δ = -322-4·4·9
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{55}}{2*4}=\frac{32-4\sqrt{55}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{55}}{2*4}=\frac{32+4\sqrt{55}}{8}
$