(2x-8)(2x+8)=52

Solution for (2x-8)(2x+8)=52 equation:

(2x-8)(2x+8)=52

We move all terms to the left:

(2x-8)(2x+8)-(52)=0

We use the square of the difference formula

4x^2-64-52=0

We add all the numbers together, and all the variables

4x^2-116=0

a = 4; b = 0; c = -116;
Δ = b2-4ac
Δ = 02-4·4·(-116)
Δ = 1856
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:

$\sqrt{\Delta}=\sqrt{1856}=\sqrt{64*29}=\sqrt{64}*\sqrt{29}=8\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{29}}{2*4}=\frac{0-8\sqrt{29}}{8}
=-\frac{8\sqrt{29}}{8}
=-\sqrt{29}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{29}}{2*4}=\frac{0+8\sqrt{29}}{8}
=\frac{8\sqrt{29}}{8}
=\sqrt{29}
$