The Board of Appeals shall have the power and duty to authorize, upon appeal made within 30 days of a denial of a building permit, change of use permit or special permit, a variation from the terms of this chapter as will not be contrary to the public interest where, owing to exceptional and extraordinary circumstances, there are practical difficulties or unnecessary hardships in the way of carrying out the strict letter of this chapter, subject to terms and conditions to be fixed by the Board of Appeals; provided, however, that no such variance shall be granted unless said Board finds that:
(a) There are practical difficulties in the physical development of the parcel, fully described in the findings of said Board, applying to the land or building for which the variance is sought, which conditions are peculiar to such land or building and have not resulted from any act of the applicant or any prior owner; and
(b) For reasons fully set forth in the findings of said Board, the aforesaid circumstances or conditions are such that the strict application of the provisions of this chapter would create unnecessary hardships and thus deprive the applicant of the reasonable use of such land or building and that the granting of the variance is necessary for the reasonable use of the land or building and that the variance as granted by said Board is the minimum variance that will accomplish this purpose.