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 (Lallouache et al., Phys. Rev E 82, 056112 (2010)). 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.