Presence of a charged wall distributes like charges (co-ions) and unlike charges (counter-ions) differently within an electrolytic solution. It is reasonable to expect that counter-ions have more population near the wall, while co-ions are abundant away from it; experiments and simulations support this. An analytical formula for the net charge-density distribution has been used widely since almost hundred years, was obtained by solving the Poisson-Boltzmann equation. However, the old formula shows excess counter-ions everywhere, cannot account for the missing co-ions satisfactorily, and clearly violates charge conservation principle. Here, I correct the distribution formula from fundamental considerations. The old derivation expresses charge-density distribution as a function of electrostatic potential through Boltzmann distribution, but missed a crucial point that the indefinite nature of electrostatic potential makes charge-density indefinite as well. We must tune electrostatic potential by adding suitable constant until the integral of charge-density becomes consistent with the net charge present in solution; old theory did not do it, that I do here. This result demonstrates how to reconcile a definite quantity to an indefinite one, when they are related. I anticipate, this result is going to have far reaching impacts on many fields like colloid science, electro-kinetics, bio-technology etc. that use the old theory