Any person claiming to be aggrieved by such plan of public works or method of financing, or both, may file complaint with the county clerk within twenty days after the publication of the plan of public works and method of financing provided for by section 31-410.01, together with a bond running to the district, with surety or sureties to be approved by the county clerk, conditioned to pay all costs that may be adjudged against such complaint, if the appeal be not sustained. Thereupon the county clerk shall make a transcript of the objections and of the report of adoption of the plan of public works or method of financing, or both, and such appellant shall, within ten days thereafter, file such transcript, in the district court of the county, and such court shall hear and determine all such objections in a summary manner as in a case in equity. All objections that may be filed shall be heard and determined by the court as one proceeding, and only one transcript of the adoption of the plan of public works shall be required.