Upon receiving a petition signed by 10 percent of the electors of the district, or by the owners of one-half of the lands comprising the district, requesting the dissolution of the district, the board of supervisors shall publish a notice once a week for two weeks in some newspaper in the principal county, and also in each affected county, giving notice that such petition has been filed with the board of supervisors, and that the board will hear such petition, and all objections thereto, at the next regular meeting of said board after the expiration of the time of publishing the notice (specifying the date), and directing all persons interested therein to show cause at such time, if any they have, why the district should not be dissolved.