I'd gotten myself into a pickle with an spreadsheet. I was revising the Karma Pool rules for my upcoming Shadowrun 3E game to make them follow a simple non-linear progression. I had decided that the first point would cost the normal 20k, then each additional point would cost 5k more than the last one. This gives a nice simple formula of y=2.4x^2+17.5x, where x is the number of Karma Pool points and y is the total coast.
Then I realised that for existing CHRs I needed to reverse the equation - if a CHR has already earned y karma, how many Karma Pool points would it be worth?
It turns out that solving that equation for x instead of for y is not as simple as I had hoped. I asked Chrissy to have a look at it for me, and she recommended asking Kathy in America, as Kathy is a Math(s) teacher.
After much hard work, Kathy tells me that the correct answer is x = SQRT((8x+245)/20)-3.5
I'd never have worked that out by myself.
Many thanks, Kathy!
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