In case a protest is filed under section 14-3,120 or 14-3,121, the city shall have the power and responsibility to hear, determine, and adjudicate the objections raised by any protest in all matters relating to regularity, legality, and sufficiency of such petition and supplemental petition upon such notice, to the party protesting, of the time, place, and purpose of the hearing as the city may from time to time provide.