Physics olympiad - electrostatics

[borgwal]

V_2-V_1=\frac{q_1}{4\pi\epsilon}(1/r-1/2r)
V_3-V_2=\frac{q_1+q_2}{4\pi\epsilon}(1/2r-1/3r)

So I add these equations?

Sorry, yes! You need V_3-V_1, and then set the result equal to zero.

 

[alexmahone]

V_3-V_1=\frac{q_1}{4\pi\epsilon r}+\frac{q_2}{4\pi\epsilon 6r}=0?

 

[borgwal]

V_3-V_1=\frac{q_1}{4\pi\epsilon r}+\frac{q_2}{4\pi\epsilon 6r}=0?

Not quite...you made a small mistake in the addition