32w^2-64=0

Solution for 32w^2-64=0 equation:

32w^2-64=0

a = 32; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·32·(-64)
Δ = 8192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{2}}{2*32}=\frac{0-64\sqrt{2}}{64}
=-\frac{64\sqrt{2}}{64}
=-\sqrt{2}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{2}}{2*32}=\frac{0+64\sqrt{2}}{64}
=\frac{64\sqrt{2}}{64}
=\sqrt{2}
$