The county board may, after public hearing on the petition, thereupon change the boundaries of the original drainage district organized under the provisions of Chapter 31, article 3 or 4, so as to include the area benefited by the drainage ditch constructed under the provisions of sections 31-101 to 31-134, or by the drainage district which has been dissolved; Provided, that the county board shall first find and determine that such change of boundaries is just and will be conducive to the public health, convenience or welfare.