512x2=1024

Solution for 512x2=1024 equation:

512x^2=1024

We move all terms to the left:

512x^2-(1024)=0

a = 512; b = 0; c = -1024;
Δ = b2-4ac
Δ = 02-4·512·(-1024)
Δ = 2097152
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:

$\sqrt{\Delta}=\sqrt{2097152}=\sqrt{1048576*2}=\sqrt{1048576}*\sqrt{2}=1024\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1024\sqrt{2}}{2*512}=\frac{0-1024\sqrt{2}}{1024}
=-\frac{1024\sqrt{2}}{1024}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1024\sqrt{2}}{2*512}=\frac{0+1024\sqrt{2}}{1024}
=\frac{1024\sqrt{2}}{1024}
=\sqrt{2}
$