Upon the filing of a petition with the board of supervisors that is signed by either (1) 50 percent or more of the table grape acreage owners who own 65 percent or more of the affected acreage or by (2) 65 percent or more of the table grape acreage owners who own 50 percent or more of the affected acreage 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.