Within sixty days after such a petition has been received by the department it shall give due notice of the holding of a referendum and shall supervise such referendum and issue appropriate regulations governing the conduct thereof. The question shall be submitted by ballots upon which the words "For terminating the existence of the (name of the soil and water conservation district to be here inserted)" and "Against terminating the existence of the (name of the soil and water conservation district to be here inserted)" shall appear with a square before each proposition and a direction to insert an X mark in the square before one or the other of the propositions as the voter may favor or oppose discontinuance of such district. All owners of land lying within the boundaries of the district shall be eligible to vote in such referendum. Only such landowners shall be eligible to vote. No informalities in the conduct of such referendum or in the matters relating thereto shall invalidate the referendum or the result thereof if notice thereof shall have been given substantially as provided in this section and the referendum shall have been fairly conducted.