We present here the exact solution of an infinite range, discrete, opinion formation model. The model shows an active-absorbing phase transition, similar to that numerically found in its recently proposed continuous version. Apart from the two-agent interactions here we also report the effect of having three-agent interactions. The phase diagram has a continuous transition line (two-agent interaction dominated) and a discontinuous transition line (three-agent interaction dominated) separated by a tricritical point. © 2011 American Physical Society.