Any qualified elector residing in the district may file a petition with the board of adjustment seeking a variance from strictly complying with the land use regulations. Copies of a petition must be served upon the chairman of the supervisors of the district where the lands are located and upon the chairman of the committee. The board shall fix a time for the hearing of the petition and cause due notice of the hearing to be given. The petitioner may appear in person, by agent, or by attorney at the hearing and the supervisors and the committee may appear and be heard. If the board determines on the facts presented at the hearing 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, the board shall make and record the determination and findings of fact as to the specific conditions that establish the great practical difficulties or unnecessary hardships. Upon the findings and determination, the board may enter an order authorizing a variance from the terms of the land use regulations in its application to the lands of the petitioner consistent with the spirit of the land use regulations, and with substantial justice and the public health, safety, and welfare.