It sounds like you want to solve the following equation for $x$, where $x$ represents the level and $y$ represents the total experience points:
$$ y = \frac{75}2 x^2 + \frac{175}2 x - 125 $$
First subtract $y$ from both sides:
$$ 0 = \frac{75}2 x^2 + \frac{175}2 x - 125 - y $$
Then multiply both sides by $2$ to simplify things. Not a necessary step, but it'll help simplify a little.
$$ 0 = 75 x^2 + 175 x - 250 - 2y $$
Now use the quadratic formula, $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a$, $b$, and $c$ are as follows:
$$ 0 = \underbrace{75}_a x^2 + \underbrace{175}_b x \underbrace{- 250 - 2y}_c $$
To be clear:
\begin{align*}
a &= 75\\
b &= 175\\
c &= -250 - 2y
\end{align*}
Finally, take only the positive root, i.e.,
$$x = \frac{-b + \sqrt{b^2 - 4ac}}{2a}$$
(explained below) and then you'll want to round your answer down to the nearest integer (also explained below).
Untested PHP code snippet example:
$y = 1100; // 1100 total experience points
$a = 75;
$b = 175;
$c = -250 - 2 * $y;
$x = (-$b + sqrt($b * $b - 4 * $a * $c)) / (2 * $a); // $x is about 4.667
$x = floor($x); // Always round down. Player is level 4 in this example.
Explanation:
The quadratic formula actually gives us two roots because of the $\pm$ sign in the numerator:
$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
But for this application we only want the $+$ sign. This is because $x$ must be positive since it represents the player's current level, but if we take the root with the $-$ sign then we'll (always) get a negative number.
This example also highlights why we always want to round down. If we rounded $4.667$ up as per the standard rounding rules, then we would get $x=5$, which means the player is level 5, but according to the total XP formula, the player can't be level 5 until the player has 1250 XP:
$$ 37.5 \cdot 5^2 + 87.5 \cdot 5 - 125 = 1250 $$
In other words, a player hasn't actually reached level 5 until the player is actually at level 5. Therefore being "close" to level 5 (e.g., being at "level 4.667") doesn't count as being at level 5.
