In this link. What do the #'s in the solution mean? Also there could be 0 to 4 solutions for given values of x, q, w, r, t and u. How do the equations provided return those up to 4 values?

W/A is built upon the Mathematica language, in which # denotes the slot symbol (a placeholder if you will). From the way I interpret the syntax (which is almost certainly going to be incorrect), the # should be replaced by a one (because of the &, 1 at the end). However, that would make no sense at all, so your guess is as good as mine. I do remember having similar output from the root function in Maple, and somehow managing to expand it into something meaningful, but I still have no clue as to what it actually means.

 

Another page you might find useful is the documentation for Root.

They look like placeholders to denote floating precision numbers, to me. That is 1# denotes 1 stored as a float, not as an integer.

 

Though, this is just my guess.

I thought everything was like a float not an integer by default as it is algebra.