a*a*2-512=0

Solution for a*a*2-512=0 equation:

a*a*2-512=0

Wy multiply elements

2a^2*2-512=0

Wy multiply elements

4a^2-512=0

a = 4; b = 0; c = -512;
Δ = b2-4ac
Δ = 02-4·4·(-512)
Δ = 8192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8192}=\sqrt{4096*2}=\sqrt{4096}*\sqrt{2}=64\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{2}}{2*4}=\frac{0-64\sqrt{2}}{8}
=-\frac{64\sqrt{2}}{8}
=-8\sqrt{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{2}}{2*4}=\frac{0+64\sqrt{2}}{8}
=\frac{64\sqrt{2}}{8}
=8\sqrt{2}
$