dave, did you find the ORIGINAL Thread? cause i can't find it. THanks for moving it.

Quite right. This is transcendental. Mr. Wolfram informs me it is a Quintic equation (of the Bring-Quintic form). So without getting into the crazy math, here's a nice way to solve this using any old graphing calculator: You need to use the "intersection" function of your calculator. You will use two equations- one is y=0 and the other is 20x + 10^x=0. Now find the intersection. Your calculator will ask, "Do you want to guess?" or something similar. This means it can't find the EXACT answer and you need to point it in the right direction. Just press yes, and you should get an answer along the lines of x= -0.045.... to about six places. I know this thread is old, but I thought I'd post this method anyway. Hope someone finds it interesting, if not helpful! =)

Why can't you just substitute x -> x*log(e) and use the Lambert W?

Quite right. I was trying to give the "most simple" method of solving. That is, if you've never heard of the Omega contant or Lambert W and still want to find a reasonable answer, here's how to go about it.