roots of a several variable for the equation $y-3x^2-y^3=0$

Question

How can I get the roots of the next equation?

$$y-3x^2-y^3=0$$

I just dont get the same answer than my teacher:

$$x = \frac {- \sqrt2}{3(3^{1/4})}, y = \frac{-2}{\sqrt3}$$

Answer 1

Any point on the graph will satisfy the equation. You might wish to verify that your teacher's solution lies on the graph by squaring the $x$, cubing the $y$ and taking the designated combination.