(2x-8)(2x+8)=50

Solution for (2x-8)(2x+8)=50 equation:

(2x-8)(2x+8)=50

We move all terms to the left:

(2x-8)(2x+8)-(50)=0

We use the square of the difference formula

4x^2-64-50=0

We add all the numbers together, and all the variables

4x^2-114=0

a = 4; b = 0; c = -114;
Δ = b2-4ac
Δ = 02-4·4·(-114)
Δ = 1824
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:

$\sqrt{\Delta}=\sqrt{1824}=\sqrt{16*114}=\sqrt{16}*\sqrt{114}=4\sqrt{114}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{114}}{2*4}=\frac{0-4\sqrt{114}}{8}
=-\frac{4\sqrt{114}}{8}
=-\frac{\sqrt{114}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{114}}{2*4}=\frac{0+4\sqrt{114}}{8}
=\frac{4\sqrt{114}}{8}
=\frac{\sqrt{114}}{2}
$