Any person or corporation feeling aggrieved thereby may appeal to the district court within and for the proper county from any final order or judgment of the board made in the proceedings and entered upon its journal determining any one of the items set forth in section 31-910. Such appeal shall be by complaint filed with the county clerk within twenty days after receipt of the notice provided for in section 31-910. The complainant shall furnish a bond running to the county to be approved by the county clerk conditioned to pay all costs that may be adjudged against the complainant if the appeal be not sustained. The county clerk shall thereupon make a transcript of the objections and the determination and such complainant shall, within ten days after receipt of such transcript, file such transcript in the district court and such court shall hear and determine such appeal in a summary manner as in a case in equity and shall increase or reduce the assessments of benefits or may increase or reduce the award of damages upon any tract where the same may be required to make the apportionment equitable. All appeals that may be filed shall be heard and determined by the court in one proceeding and only one transcript of the determination shall be required.