A portion of a soil and water conservation district, such portion being composed of one or more entire counties, may withdraw from such district and constitute itself a separate soil and water conservation district by the procedure set forth in this section and §§ 48-9-830 and 48-9-840. A petition signed by a majority of the members of the governing body of the soil and water conservation district or a petition signed by twenty-five landowners of the county or counties wishing to withdraw and constitute themselves a separate district may be filed with the department asking that the subdivision be made and constitute a district. Such petition shall (a) set forth the name of the district, (b) describe the existing boundary lines of the district and boundary lines of the proposed district (subdivision) and (c) request that the department hold a public hearing upon the question of the proposed subdivision and that the department duly define the boundary lines as set out in the petition.