512=x^2/3

Solution for 512=x^2/3 equation:

512=x^2/3

We move all terms to the left:

512-(x^2/3)=0

We get rid of parentheses

-x^2/3+512=0

We multiply all the terms by the denominator


-x^2+512*3=0

We add all the numbers together, and all the variables

-1x^2+1536=0

a = -1; b = 0; c = +1536;
Δ = b2-4ac
Δ = 02-4·(-1)·1536
Δ = 6144
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:

$\sqrt{\Delta}=\sqrt{6144}=\sqrt{1024*6}=\sqrt{1024}*\sqrt{6}=32\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{6}}{2*-1}=\frac{0-32\sqrt{6}}{-2}
=-\frac{32\sqrt{6}}{-2}
=-\frac{16\sqrt{6}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{6}}{2*-1}=\frac{0+32\sqrt{6}}{-2}
=\frac{32\sqrt{6}}{-2}
=\frac{16\sqrt{6}}{-1}
$