jmc

We square both sides to get rid of the square root sign. This gives us $2-3z=81$. Solving for $z$ gives $z=\boxed{-\frac{79}{3}}$. We squared an equation, so we have to test our solution to make sure it isn't extraneous. We have $$\sqrt{2-3\left(-\frac{79}{3}\right)}=\sqrt{2+79}=9,$$so our solution is valid.