Can you check this? - Charges and Forces

[Albeaver]

Can you check this? -- Charges and Forces...

Homework Statement

A +3-mC charge and a -4-mC charge are fixed in position and separated by 5 meters.
A)Where could a +7-mC charge be placed so that the net force on it is zero?
B)Where could a -7-mC charge be placed so that the net force on it is zero?

I came up with this diagram:
|---------------5m------------------|
*----------------*------------------*
q[1] q[2] q[3]
|-------r[1]------|----------r[2]----|

Homework Equations

F[1]=K(|q[1]*q[2]|)/r[1]^2
F[2]=K(|q[2]*q[3]|)/r[2]^2
r[1]+r[2]=5
k=8.99*10^9
|q[1]|=4
|q[3]|=3
|q[2]|=7

The Attempt at a Solution

F[1]=F[2]<---Because they are equal
K(q[1]*q[2])/r[1]^2=K(q[3]*q[2])/(5-r[1])^2<---We get (5-r[1])=r[2] from r[1]+r[2]=5 solved for r[2])
Then after we solve for r[1] we get this:
r[1]=5*√(q[3])*(√(q[3])-√(q[₁]))/(q[3]-q[1])

So that means that both the +7-mC charge and the -7-mC charge are in the same position. The number I got was r[1]=2.32m and r[2]=2.68m. Did I set this up, and execute this correctly?
Thank you very much for your time.

 

[barryj]

With a +3 on the left and a-4 on the right, is there any position between the two where the net force will be zero? Maybe the position is to the left or right of both charges.