In my game you can spend points to upgrade characteristics. Each characteristic has a formula like:
A) out = in : for one point spent, one pont gained (you spend 1 point on Force so your force goes from 5 to 6)
B) out = last level (starting at 1) : so the first point spent earns you 1 point, the next point spent earns you an additional 2 and so on (+3,+4,+5...)
C) The inverse of B) : You need to spend 1 point to earn one, then you need to spend 2 to earn another one and so on.
I have already found the formula for calculating the actual level of B when points spent = x :
charac = (x*(x+1))/2
But I'd like to know what the "reverse" version of B) (usable for C) is, ie. if I have spent x points, how many have I earned if 1 spent gives 1, 1+2=3 gives 2, 1+2+3=6 gives 3 and so on.
I know I can just calculate the numbers but I'd like to have the formula because its neater and so that I can stick it in an excel sheet for example...
ps. I think I have nailed it down to something like charac = sqrt( x*m +k) but then I'm stuck doing number guessing for k and m and I feel I might be wrong anyway as I get close but never hits the spot.