CONTEST: Solve this and win!

[DPI Wizard]

I know there's quite a few very skilled people here, so if anyone can solve this problem, there's a €20 Steam Gift Card in it for you 

 

Solve this equation for x:

 

[Link]

 

In other words; a, b and y are known, and the equation to calculate x is needed.

 

If you think you got it, you can verify it with these two examples, which Wolfram|Alpha manages to solve but doesn't show how (ignore rounding of x):

 

 | x = 1.33 [Link]

 

| x = 0.5 [Link]

 

This is a simplification of the equation used to calculate the zoom sensitivity coefficient for BF1/BF4.

 

Rules: The first person to post a working solution wins.

 

Any takers?

[mattiasheen]

It's impossible ( http://www.wolframalpha.com/input/?i=inverse+y(x)%3Darctan(ax)%2Farctan(bx) )

You can recast the function in a few forms, but none help. For example

y(x) = log(1 - alpha)/log(1 - beta) for alpha = iax and beta = ibx

Edited November 1, 2016 by mattiasheen

[DPI Wizard]

It's impossible ( http://www.wolframalpha.com/input/?i=inverse+y(x)%3Darctan(ax)%2Farctan(bx) )

I initially though so as well, but Wolfram solves the two examples somehow. It might require some serious code though... The rounding of the results are because the input is rounded.

 

I might look into the Wolfram API

[DPI Wizard]

I've gotten a possible solution to this in a PM btw, will test it later today!

[SevenFreak]

My calculator can solve it too but I can´t - what I´ve read is that you might need to use addition theorems in order to solve the equation

[DPI Wizard]

Big thanks to Skwuruhl who came up with a brilliant solution to this problem!