Finding Equilibrium Position for Third Charge in Line of Point Charges

[map7s]

Homework Statement

Two point charges lie on the x axis. A charge of +8.4 µC is at the origin, and a charge of -3.8 µC is at x = 10.0 cm.
At what position x would a third charge q3 be in equilibrium?

Homework Equations

F=(kq1 q2)/r^2

The Attempt at a Solution

I think that my main problem was that I wasn't quite sure how to solve for the distance if I don't have the charge for the third particle or its relation to the other charges.

 

[drpizza]

Then, simply use q3 as the value each time you plug it into your relevant equation. It should cancel out later.

 

[map7s]

I tried that, but the q3 doesn't cancel out and I don't know how to get rid of it because they don't state any relationships between the charges. (ex: q1=q, q2=-3q, etc.)