# Use the implicit function theorem to determine when can the following equation be solved:

I was asked to determine when the equation $f(x,y)=y^2+y+3x+1=0$ for $y$ in terms of $x$. First the I was asked to provide and answer without using the Implicit Function Theorem (IFT), so I simply analyzed it as a quadratic equation and concluded that the equation had real solutions iff $1-4(1)(3x+1)\geq 0$ which means that $x\geq -1/4$.

The second part of the problem ask you to apply the IFT to determine the exact same thing, in order to compare both results. I know what the IFT states, its just that I'm not sure how using it can help me solve $y$ in terms of $x$.