X^2+16^2=8x^2

Solution for X^2+16^2=8x^2 equation:

X^2+16^2=8X^2

We move all terms to the left:

X^2+16^2-(8X^2)=0

We add all the numbers together, and all the variables

-7X^2+256=0

a = -7; b = 0; c = +256;
Δ = b2-4ac
Δ = 02-4·(-7)·256
Δ = 7168
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:

$\sqrt{\Delta}=\sqrt{7168}=\sqrt{1024*7}=\sqrt{1024}*\sqrt{7}=32\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{7}}{2*-7}=\frac{0-32\sqrt{7}}{-14}
=-\frac{32\sqrt{7}}{-14}
=-\frac{16\sqrt{7}}{-7}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{7}}{2*-7}=\frac{0+32\sqrt{7}}{-14}
=\frac{32\sqrt{7}}{-14}
=\frac{16\sqrt{7}}{-7}
$