Calculating experience for a text-based RPG - php

Question

OK, using the answers over at this question I was able to produce the following code to calculated the experience needed to level on a text-based RPG I am working on. I'll say from the get-go that my math skills are not great, so please "dumb it down" as much as you can.
function calcExp($L) {
if($L <= 5) {
//If Level 5 or less then just 12 exp per level
return 12*$L;
}
if($L > 1000) {
//If over level 1,000, we need to slow them down
//add an additional 500k per level required
$calc = $L - 1000;
$c2 = 500000*$calc;
return (5*$L*$L-5*$L)+$c2;
}
else {
//otherwise, calculate as follows
$exp = 5 * $L * $L - 5 * $L;
return $exp;
}
}
That returns the correct amount of experience, now I'm trying to figure out how to reverse the process so that I can checkLvl($EXPERIENCE) and have it return the level it should be at.
So then if I were to
$level = 10;
$exp = 450;
$check = checkLvl($exp);
if($check != $level) { die('Unknown Error'); }
else { echo "Success!"; }
Note: the above code is just me trying to be clear.
I'm at a loss as to how to reverse the little mess I created.

Answer 1

Your first five levels are only tweleve exp per level, so you could reverse and say the first 60 exp (5 * 12) should be floor($exp / 12)
Your second level range is from 6 to 1000. So if the exp is greater than 60, but less than whatever exp you need for level 1000, you'd solve $exp = 5 * $L * $L - 5 * $L for $L, which is a quadratic equation. It would look something like $L = (5 + sqrt(25 - 4 * 5 * -$exp)) / (2 * 5)
Everything else above level 1000 should solve a similar quadratic equation, $exp = (5 * $L * $L - 5 * $L) + 500000 * ($L - 1000) for $L. It would look like $L = ((5 + 500000) + sqrt((5 + 500000)^2 - 4 * 5 * (500000 - $exp))) / (2 * 5)