Question 465556
To find the value of q in which equilibrium happens, must have

{{{50/(q+5) = q/10 + 4.5}}}.

==>500 = (q+5)(q + 45), after cross-multiplication
==> {{{0 = q^2 + 50q - 275}}}, after further simplification.
==> (q-5)(q+55) = 0 ==> q = 5.  (Eliminate q = -55).

when q = 5, demand and supply are both equal to 5.

==> Consumer's surplus = {{{int( (50/(q+5) - 5), dq, 0,5) = (50ln(q+5) - 5q)[0]^5 = 50ln2 - 25 = 9.66}}}, to 2 decimal places.

==> Producer's surplus = {{{int( (5 - (q/10 + 4.5)), dq, 0,5) = int( (5.5 - q/10), dq, 0,5) = (5.5q - q^2/20)[0]^5 = 26.25}}}.