Your problem depends on three variables pa, pb, pbdev and it has one equation and one inequality, all of them polynomial. It seems hard to solve symbolically. You can explore the solution set visually:
ContourPlot3D[Evaluate[D[pidev, pbdev] == 0],
{pbdev, 0, 10}, {pa, 0, 10}, {pb, 0, 10},
RegionFunction -> Function[{pbdev, pa, pb},
Evaluate[D[D[pidev, pbdev], pbdev] < 0]],
AxesLabel -> Automatic]
