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I'm trying to come up with an equation to determine what level you are when you have a certain amount of experience in an online game. I tried using quickmath.com and wolframalpha.com to figure out the steps but neither shows how they got there. The formula the game uses to determine experience required for level is:

$$ \frac{50}{3} (x^3-6x^2+17x-12)$$

Where x is level

If I know the experience I have (say 37800) I can work it back a ways but then I get stuck. Just hoping for a nudge in the right direction

$$ \frac{50}{3} (x^3-6x^2+17x-12) = 37800 $$ $$ \frac{50\div50}{3} (x^3-6x^2+17x-12) = 37800\div50 $$ $$ 3*3\div (x^3-6x^2+17x-12) = 756*3 $$ $$ x^3-6x^2+17x-12+12 = 2268+12 $$ $$ x^3-6x^2+17x = 2280 $$

This is the point where I get lost quickmath.com shows the next step as: $$ x=\frac{-(\sqrt{527}*I+9)}2 $$

But I have not got the foggiest how they got there.

Matthew Brown
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1 Answers1

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Your equation $$x^3-6x^2+17x - 2280=0$$ is perfectly correct; it is a cubic and to solve it, you could use Cardano method which will tell you that there are one real root and two complex roots. They are respectively $$x_1=15 \qquad , \qquad x_{2,3}=\frac{1}{2} \left(-9\pm i \sqrt{527}\right)$$ I do not suppose that you care about the complex solution so $x=15$ is your solution.

If you need to solve for $x$ equation $$\frac{50}{3} (x^3-6x^2+17x-12)=p$$ the only real solution will be $$x=2+\frac{A^2-50 \sqrt[3]{30}}{30^{2/3} A}$$ where $$A=\sqrt[3]{27 (p-100)+\sqrt{3} \sqrt{243 (p-200) p+3680000}}$$

Claude Leibovici
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  • I will Have to research the Cardano Method! Thank you. I am interested in the complex solution as I need a formula for a spreadsheet I am making. – Matthew Brown Aug 16 '16 at 05:55
  • what do you want to do with complex solutions ? whatever $p$ would be, there is only one real solution; – Claude Leibovici Aug 16 '16 at 07:09
  • I have a spread sheet that calculates experience gains and predicts what your final experience will be on a certain date. I would like to then take the final experience and from that calculate the player’s level to avoid having to reference a second table. So basically I am trying to use what you have given me to create a formula in excel to calculate level based on experience. – Matthew Brown Aug 16 '16 at 18:48
  • It took a while but I got it converted to an excel formula and it works like a charm thank you! – Matthew Brown Aug 18 '16 at 00:23