32^6-2x^2=0

Solution for 32^6-2x^2=0 equation:

32^6-2x^2=0

We add all the numbers together, and all the variables

-2x^2+1073741824=0

a = -2; b = 0; c = +1073741824;
Δ = b2-4ac
Δ = 02-4·(-2)·1073741824
Δ = 8589934592
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:

$\sqrt{\Delta}=\sqrt{8589934592}=\sqrt{4294967296*2}=\sqrt{4294967296}*\sqrt{2}=65536\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-65536\sqrt{2}}{2*-2}=\frac{0-65536\sqrt{2}}{-4}
=-\frac{65536\sqrt{2}}{-4}
=-\frac{16384\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+65536\sqrt{2}}{2*-2}=\frac{0+65536\sqrt{2}}{-4}
=\frac{65536\sqrt{2}}{-4}
=\frac{16384\sqrt{2}}{-1}
$