(1) The board of adjustment appointed pursuant to section 19-907 shall, subject to such appropriate conditions and safeguards as may be established by the city council or village board of trustees, have only the following powers: (a) To hear and decide appeals when it is alleged there is error in any order, requirement, decision, or determination made by an administrative official or agency based on or made in the enforcement of any zoning regulation or any regulation relating to the location or soundness of structures, except that the authority to hear and decide appeals shall not apply to decisions made under subsection (3) of section 19-929; (b) to hear and decide, in accordance with the provisions of any zoning regulation, requests for interpretation of any map; and (c) when by reason of exceptional narrowness, shallowness, or shape of a specific piece of property at the time of the enactment of the zoning regulations, or by reason of exceptional topographic conditions or other extraordinary and exceptional situation or condition of such piece of property, the strict application of any enacted regulation under this section and sections 19-901, 19-903 to 19-904.01, and 19-908 would result in peculiar and exceptional practical difficulties to or exceptional and undue hardships upon the owner of such property, to authorize, upon an appeal relating to the property, a variance from such strict application so as to relieve such difficulties or hardship, if such relief may be granted without substantial detriment to the public good and without substantially impairing the intent and purpose of any zoning regulation.
(2) No such variance shall be authorized by the board of adjustment unless it finds that: (a) The strict application of the zoning regulation would produce undue hardship; (b) such hardship is not shared generally by other properties in the same zoning district and the same vicinity; (c) the authorization of such variance will not be of substantial detriment to adjacent property and the character of the district will not be changed by the granting of the variance; and (d) the granting of such variance is based upon reason of demonstrable and exceptional hardship as distinguished from variations for purposes of convenience, profit, or caprice. No variance shall be authorized unless the board of adjustment finds that the condition or situation of the property concerned or the intended use of the property is not of so general or recurring a nature as to make reasonably practicable the formulation of a general regulation to be adopted as an amendment to the zoning regulations.
(3) In exercising the powers granted in this section, the board of adjustment may, in conformity with sections 19-901 to 19-915, reverse or affirm, wholly or partly, or may modify the order, requirement, decision, or determination appealed from, and may make such order, requirement, decision, or determination as ought to be made, and to that end shall have all the powers of the officer from whom the appeal is taken. The concurring vote of four members of the board of adjustment shall be necessary to reverse any order, requirement, decision, or determination of any such administrative official, or to decide in favor of the applicant on any matter upon which it is required to pass under any such regulation or to effect any variation in such regulation.