When a majority of the governing bodies of each of the cities desires consolidation, or petitions signed by the requisite number of qualified electors in each city have been duly received and recorded by each city, a joint resolution signed by the respective mayors, shall set a time for a special election to be held in each of the cities desiring consolidation. The election shall be held on the next date authorized by section 50-405, Idaho Code, which is more than forty-five (45) days after final adoption, of the joint resolution.