> I'm expecting it to be infinity or -infinity I think but there's -infinities and +sqrt(infinities) so I got no idea

That will often be the case, but not here. You have 'a' in two places: -a, and sqrt(a^(2) and other stuff): the sqrt(a^(2) and other stuff) is going to approach a, and the -a and a will almost cancel out.

In general, if you have something that looks like -x + sqrt(x^2 + bx + c), you complete the square:

-x + sqrt(x^2 + bx + c)

-x + sqrt( x^2 + bx + b^2/4 - b^2/4 + c)

-x + sqrt((x + b/2)^2 + c-b^2/4)

Now the square root term approaches x+b/2 as x-->infinity, the -x and +x cancel, and the whole thing approaches b/2.

You have essentially that same question here: your c, e, x, 2, pi, 4, and 61.3 are all constants.