x^2=8^6

Solution for x^2=8^6 equation:

x^2=8^6

We move all terms to the left:

x^2-(8^6)=0

We add all the numbers together, and all the variables

x^2-262144=0

a = 1; b = 0; c = -262144;
Δ = b2-4ac
Δ = 02-4·1·(-262144)
Δ = 1048576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1048576}=1024$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1024}{2*1}=\frac{-1024}{2}
=-512
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1024}{2*1}=\frac{1024}{2}
=512
$