How can we solve this 3rd degree equation where the unknown is $x\ge0$ and a,y constants
$\frac{x^3}{9a^2}-\frac{2x^2}{3}+a^2x-y^2=0$

The above equation comes from the main problem which is to express this formula $y=(\frac{x}{3a}-a)\sqrt x$ as term of x

Is there any other way to express the second formula as term of x except to solve the first 3rd grade equation??