How to reverse a certain formula I've got this formula which gives me the experience required for a specific level.
$25X^2-25$
Which gives me a nice experience table like this
Experience from level X to X+1
From level 4 to 5, 600 experiences are required
What I keep track of is the total experience a player has gained
To Next Level    Total Experience Gained
1: 0             0
2: 75            75
3: 200           275
4: 375           650
5: 600           1250
6: 875           2125
etc

I believe it's quadratic or something, I am not very good at maths.
But how can I turn it around, and find what level the player is?
New example
If a player has a total experience of 1000, that would put him at level 4, because 1000 is between 650 and 1250.
Edit
My bad, I explained too poorly, I am sorry, please read again
 A: Old question
$$y=25x^2-25 \Rightarrow x=\pm\sqrt{\frac{y}{25}+1}$$
But in your case a level is always positive and is an integer. Thus, the level is given by the formula :
$$\Bigl\lfloor \sqrt{\frac{y}{25}+1}\Bigr\rfloor$$
For example if you have $111$ experience, you are level $\Bigl\lfloor \sqrt{\frac{111}{25}+1}\Bigr\rfloor=\lfloor \sqrt{4.44+1}\rfloor=\lfloor \sqrt{5.44}\rfloor=2$
New question
The total experience needed to reach the level $n$ is given by :
$$\sum_{i=1}^n(25i^2-25)=-25n+25\sum_{i=1}^ni^2=-25n+25\frac{n(n+1)(2n+1)}{6}=\frac{25}{3}n^3+\frac{75}{6}n^2-\frac{125}{6}n$$
So if you have $y$ experience you need to find the positive real root of the polynomial : $\frac{25}{3}X^3+\frac{75}{6}X^2-\frac{125}{6}X-y$. You can for example try to use Cardano formula, be the result won't be very nice, or compute the result with a software. And if you take the floor of this root you have the level of of the player.
For example if you have $1000$ experience, if you solve $\frac{25}{3}X^3+\frac{75}{6}X^2-\frac{125}{6}X-1000$ in wolfram alpha it gives you the root $≈4.6322$, so the player is indeed level $4$.
