Any one or more owners of land seeking such cancelation or adjustment of taxes, or any irrigation or drainage district or incorporated water company having such lands within its project, may file with the clerk of the board of county commissioners a petition setting forth the facts upon which it is claimed a cancelation or adjustment of the taxes should be made. If the petition sets forth the facts required to be contained therein under section 31-901, the board shall hear the proof submitted in support of said petition and anyone present shall have a right to be heard in opposition thereto. If the board, after considering the evidence offered at such hearing, and at any adjournment thereof, and after making such other investigation as it may deem necessary, finds that the public interest and common welfare require that such taxes be canceled or otherwise adjusted and that such action will not be detrimental to the interests of the county and other tax-levying bodies affected thereby, and that the conditions set forth in subdivisions (a), (b) or (c) of section 31-901 exist, the board shall make and enter an order which shall be recorded in full in the official minutes of the board, setting forth its findings and decision, and its reasons therefor.