The boundaries of any district organized under the provisions of sections 46-501 to 46-573 may be changed in the manner herein prescribed, but the changes of boundaries of the district shall not impair or affect its organization, its right in or to property, or any of its rights or privileges whatsoever and shall not affect, impair, or discharge any contract, obligation, lien, or charge for or upon which it might be liable or chargeable had such change of boundaries not been made. The owners of lands may file with the board a petition, in writing, asking that such lands be included in the district. The petition shall describe the tracts or body of land owned by the petitioners. It shall be deemed to give assent by the petitioners to the inclusion in the district of the lands described in the petition. The petition shall be acknowledged in the same manner that conveyances of land are required to be acknowledged. The secretary of the board shall cause notice of the filing of such petition to be given and published in the county in which the lands are situated, which notice shall state the filing of such petition, names of petitioners, descriptions of lands mentioned, and the prayer of the petitioners and give notice to all persons interested to appear at the office of the board at the time named in the notice and show cause in writing, if any, why the petition should not be granted. The board shall at the time and place mentioned or at such time or times to which the hearing may be adjourned proceed to hear the petition and all objections presented in writing by any person showing cause why the petition should not be granted. The failure of any person interested to show cause in writing shall be deemed and held and taken as an assent on his or her part to the inclusion of such lands in the district as prayed for in the petition. If the petition is granted, the board shall make an order to that effect.