Rewrite a west to east parabola in standard form

Question

$$8y^2+96y-12x+240=0$$

I'm not sure how to approach that problem because there's a $\frac23y^2$ to deal with

Answer 1

It sounds like you need to rewrite it in the form $$(y-k)^2=4p(x-h),$$ for some constants $h,k,p$. As a hint: start with $8y^2+96y=12x-240$ and complete the square on the left-hand side (after dividing everything by $8$, if you prefer).