Upon the filing of a petition with the board of supervisors, signed by 50 percent or more of the owners of 65 percent or more of the affected land, or signed by 65 percent or more of the owners of 50 percent or more of the affected land, requesting the dissolution of the district, the board of supervisors shall set a time and place for hearing on the petition, which shall not be less than 20 days, or more than 40 days, after the filing of the petition. Immediately following the hearing, the board of supervisors shall vote on the petition for dissolution. A majority vote supporting the petition by the supervisors will result in dissolution of the district.