At the hearing to consider the proposed improvements and assessments, the governing body of any city with a population of three hundred fifty thousand inhabitants or more which is located in more than one county, or the governing body of the county of the first classification without a charter form of government that has a population of at least one hundred sixty thousand inhabitants, or the governing body of any county of the first classification without a charter form of government containing a portion of a city with a population of at least three hundred fifty thousand inhabitants, or the governing body of any county of the first classification without a charter form of government as of August 28, 1995, that has a population of more than one hundred five thousand but less than one hundred twenty thousand inhabitants, shall hear and pass upon all objections to the proposed improvements and proposed assessments, if any, and may amend the proposed improvements, and the plans and specifications therefor, or assessments as to any property, and thereupon by resolution the governing body of such city or county shall order that the improvement be made and direct that financing for the cost thereof be obtained as provided in sections 249.925 to 249.955. All assessments established in sections 249.925 to 249.955 may be appealed by the property owner to the county board of equalization and as further provided in chapter 138.