Determine the position of the charge for equilibrium
The equilibrium is not stable, but it's possible like a pyramid standing upside down in a perfect balance. 

The positive charges push each other as much as the negative charge pulls them. In addition the negative charge must get the same pull from both positive charges.

Write these as equations. This can also be formulated as a potential well or merely potential enerqy terrace (=flat point) but I believe it finally reduces to the same equations when you try to determine, where the derivative of the potential enerqy vs. position is zero and can be zero.