When the concentration of solute and solvent are equal on both sides of the membrane. It has achieved a state of osmotic equilibrium.?

Yes it is true, that when a solute and solvent are equal on both sides of the membrane it has achieved an osmotic equilibrium. Osmosis refers to the spontaneous movement of solvent molecules through a semi-permeable membrane. Usually the movement is that the solvent moves from a higher solute concentration into a direction that it tends to equalize both solute concentrations on both sides.