Trying to solve an equation I thought of.

This is my first time trying to post images and have had horrible luck, so the best I can do is just post the link to my photobucket picture. I had much difficulty fighting with the coding commands on this forum, so I created this from word.

Anyway, when I took pre-calculus algebra (aka college algebra), it seemed like concepts were always presented to us in easily-solvable forms, which rarely yielded ugly numbers.

I came up with this equation and am curious as to how it can be solved. Although I'm sure the algebra is a complete mess on this, does this problem require anything more than algebra (aka calculus, differential equations, etc.)? I just completed calculus 2 and have no idea how to tackle this problem, other than graphing it to find a decimal approximation at x-intercepts.

Is it possible to solve this equation getting exact numbers (aka fractions and logarithms without variables in them)? Or are there some equations that just cannot be solved with exact answers (and I'm referring to equations with one variable, not differential equations). I'm eager to see how this equation could be solved. Thanks.

Here is the link to this equation (again I wish I could post it here, but I haven't been able to):

NOTICE: the 13/7 inside the root is taken to the 0.13x power, not 13 taken to that power then divided by 7.

UnsolvableEquation.jpg picture by b4bis91 - Photobucket