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Homework template is missing because this was moved from a non-homework forum

Hello everyone. Hopefully someone would be able to help me with this problem.

The question states:

Two point charges q

I used a sum of forces model to answer the first part..

starting with Fac + Fbc = 0... which got me to

kqaqc/r^2 = -kqbqc/(x+r)^2

some things canceled.. ended up with a quadratic...

came to the conclusion that r = 0.16 m or -.051 m.

I'm fairly confident in that answer but I am now not sure how to find the charge of qc. Modeling it as a sum of forces would just cancel the qc...

The question states:

Two point charges q

_{a}= -12 micro coulombs and q_{b}= 45.0 micro coulombs and a third particle with unknown charge qc are located on the x axis. The particle qa is at the origin placed so that each particle is in equilibrium under the particles. Find the required location and the magnitude and the sign of the charge of the third particle...I used a sum of forces model to answer the first part..

starting with Fac + Fbc = 0... which got me to

kqaqc/r^2 = -kqbqc/(x+r)^2

some things canceled.. ended up with a quadratic...

came to the conclusion that r = 0.16 m or -.051 m.

I'm fairly confident in that answer but I am now not sure how to find the charge of qc. Modeling it as a sum of forces would just cancel the qc...