The board of adjustment may:
(1) Hear and decide appeals if it is alleged there is error in any order, requirement, decision, or determination made by an administrative official in the enforcement of this chapter or of any ordinance adopted pursuant to this chapter;
(2) Authorize upon appeal in specific cases a variance from the terms of the ordinance that is not contrary to the public interest, if, owing to special conditions, a literal enforcement of the provisions of the ordinance will result in unnecessary hardship and so that the spirit of the ordinance is observed and substantial justice done; and
(3) Hear and determine conditional uses as authorized by the zoning ordinance. The uses shall be determined by an affirmative majority vote of the present and voting members of the board of adjustment.