Solving $x = 5(y^2+10y+20)$ for $y$

Question

I have an equation:

$$x = 5(y^2+10y+20)$$

For context, $y$ is a value that represents the current level of a user. The equation is looking for $x$, i.e finding how much experience ($x$) is required to achieve the inputted level $y$.

My goal is to reverse this:

$$y=something ...$$

In doing so, I would be able to find the given level (y), with the inputted XP (x).

I am unsure of where to go from in order to do so. Upon trying to isolate by 'common' means (reversing actions until I can isolate), I'm left with answers that I cannot further simplify, or at least am unsure how to. Any help would be appreciated.

Answer 1

First, isolate the quadratic term: $$\frac{x}{5} = y^2 + 10y + 20$$ Then you can complete the square by adding 5 to both sides: $$\frac{x}{5} + 5 = y^2 + 10y + 25 = (y+5)^2$$ Finally, you can take the square root and subtract 5 from both sides: $$\pm\sqrt{\frac{x}{5} + 5} - 5 = y$$

Answer 2

$$5y^2+50y+(100-x)=0$$ solve for $y$ using the quadratic formula.