The board shall fix a time for the hearing of the petition and cause due notice of such hearing to be given. The commissioners of the district and the department may appear and be heard at such hearing. Any occupier of lands lying within the district who shall object to the authorizing of the variance prayed for may intervene and become a party to the proceedings. Any party to the hearing before the board may appear in person, by agent or by attorney. If, upon the facts presented at such hearing, the board shall determine that there are great practical difficulties or unnecessary hardships in the way of applying the strict letter of any of the land-use regulations upon the lands of the petitioner, it shall make and record such determination and shall make and record findings of fact as to the specific conditions which establish such great practical difficulties or unnecessary hardships. Upon the basis of such findings and determination the board may by order authorize such variance from the terms of the land-use regulations, in their application to the lands of the petitioner, as will relieve such great practical difficulties or unnecessary hardships and will not be contrary to the public interest and such that the spirit of the land-use regulations shall be observed, the public health, safety and welfare secured and substantial justice done.