x^2=4^6

Solution for x^2=4^6 equation:

x^2=4^6

We move all terms to the left:

x^2-(4^6)=0

We add all the numbers together, and all the variables

x^2-4096=0

a = 1; b = 0; c = -4096;
Δ = b2-4ac
Δ = 02-4·1·(-4096)
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-128}{2*1}=\frac{-128}{2}
=-64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+128}{2*1}=\frac{128}{2}
=64
$