Question

Charges q1 and q2 lie on x axis at points x= -a and x= 5, respectively.
(a) how must q1 and q2 be related for the net force on charge +Q at x = a/2 to be zero ?
(b) and if +Q is placed at x = 3a/2.

Answer 1

Q at a/2
d1 = 1.5 a
d2 = 5 -.5 a

for same E field from each at a/2 (both + charges)
q1/d1^2 = q2/d2^2
d1/2.25a^2 =q2/(25 - 5a+.25a^2)

by the way, unless you mean 5a and not 5, the problem is not well defined. q1 and q2 must be same sign if Q is between them and of opposite signs if Q is to the right of 5

Answer 2

Ops I meant the other x is (a)
My bad