How long does it take for paranoid delusions to dissapear once you have found the root cause?

It depends: It depends on what that root cause is. If schizophrenia, one would need antipsychotic medicines at optimal, consistent dosing for a time. If it's a recreational drug, one hopes the delusions will quiet down once the drug is out of system - but in the case of marijuana and some hallucinogens, these may persist. If mania or psychotic depression, delusions should leave when mood problem remits.