As you suggest, your problem neatly divides into two parts and you can take the partial of each of those.
Adding those two results gives
Solve[1.28 (1.92 a n (1458.33+F+2.33333 U)+(32+3 a (n-4) n)(2976+7.382 B+10.6 U)(0.37-0.315/x^1.5)) +
(0.652797 a n^5 p S^2)/(F^2 U^2)+(1.1869 p (2 a (n^2-n) S^2+a (n-2)(n+n^2) S^2)(0.33-0.335/x^1.5))/(B U^2)==0,x]
and that is small enough to fit into WolframAlpha.
Unfortunately the powers of x in the denominator seem to be too much for either WolframAlpha or Mathematica to quickly solve.
Since x seems to only appear in two places as 1/x^1.5 I try a substitution
Solve[1.28 (1.92 a n (1458.33+F+2.33333 U)+(32+3 a (n-4) n)(2976+7.382 B+10.6 U)(0.37-0.315 q)) +
(0.652797 a n^5 p S^2)/(F^2 U^2)+(1.1869 p (2 a (n^2-n) S^2+a (n-2)(n+n^2) S^2)(0.33-0.335 q))/(B U^2)==0,q]
Unfortunately I have not been able to find a way to coax WolframAlpha into solving that, but I suspect it should be able to do that with the appropriate posing of the question.
Fortunately Mathematica is less reluctant.
In[9]:= Simplify[Solve[1.28 (1.92 a n (1458.33+F+2.33333 U)+(32+3 a (n-4) n) (2976+7.382 B+10.6 U)
(0.37-0.315 q))+(0.652797 a n^5 p S^2)/(F^2 U^2)+(1.1869 p (2 a (n^2-n) S^2+a (n-2) (n+n^2) S^2)
(0.33 - 0.335 q))/(B U^2) == 0, q]]
Out[9]= {{q -> (-((0.652797 a n^5 p S^2)/(F^2 U^2)) - (0.391677 a n (-4.+1. n+n^2) p S^2)/(B U^2) -
2.4576 a n (1458.33+F+2.33333 U)-0.4736 (32.+3. a (-4.+n) n) (2976.+7.382 B+10.6 U))/
(-((0.397612 a n (-4.+1. n+n^2) p S^2)/(B U^2))-0.4032 (32.+3. a (-4.+n) n) (2976.+7.382 B+10.6 U))}}
I think with some fiddling you should be able to get WolframAlpha to give you the same result.
A couple of tricks that can sometimes help you if you at the limit of what WolframAlpha will accept:
WolframAlpha usually interprets x2 or c2 as x squared or c squared but does not interpret (x+y)2 as (x+y) squared. That can sometimes save you a few characters if the length of your input is slightly too long.
WolframAlpha seems to sometimes do better when variables are named x or sometimes y or z while coefficients are named single lowercase letters from the beginning of the alphabet, but watch out for it sometimes interpreting e as Euler's constant, although it seems to usually ask if that is correct.
