6x^2=512

Solution for 6x^2=512 equation:

6x^2=512

We move all terms to the left:

6x^2-(512)=0

a = 6; b = 0; c = -512;
Δ = b2-4ac
Δ = 02-4·6·(-512)
Δ = 12288
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:

$\sqrt{\Delta}=\sqrt{12288}=\sqrt{4096*3}=\sqrt{4096}*\sqrt{3}=64\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-64\sqrt{3}}{2*6}=\frac{0-64\sqrt{3}}{12}
=-\frac{64\sqrt{3}}{12}
=-\frac{16\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+64\sqrt{3}}{2*6}=\frac{0+64\sqrt{3}}{12}
=\frac{64\sqrt{3}}{12}
=\frac{16\sqrt{3}}{3}
$