When the council of any city having less than thirty thousand inhabitants and having a special charter shall deem it necessary to pave, macadamize, gutter, curb, grade or otherwise improve the roadway of any street, avenue or alley, or other highway, or any part thereof, within the limits of the city, for which a special tax is to be levied as provided in section 88.777, the council shall, by resolution, declare such work or improvements necessary to be done, and shall cause plans and specifications for such work and improvements, together with an estimate of the cost thereof, to be prepared by the city engineer or other proper officer, and filed with the city clerk of such city, subject to the inspection of the public, and shall cause such resolution to be published in some newspaper printed in the city for two consecutive insertions in a weekly paper or seven consecutive insertions in a daily paper and if a majority of the resident owners of the property liable to taxation therefor, at the date of the passage of such resolution, who shall own a majority of the front feet owned by residents of the city abutting on the street, avenue or alley proposed to be improved, shall not, within ten days thereafter, file with the clerk of the city, their protest against such improvements, then the council shall have power to cause a contract for said work to be let to the lowest and best bidder, on the plans and specifications filed as aforesaid with the city clerk by the city engineer or other proper officer, not less than one week’s advertisement for bids thereon being made in some newspaper published in the city. Where the bids for said work are above the estimates, or no bids are presented, or where the bids presented are for any reason rejected, or where the contractor to whom the contract is awarded fails to enter into a written contract for the performance of said contract, or to execute the bonds required by ordinance within the time provided therefor, the council may readvertise for bids. When the council shall by ordinance find and declare that a majority of the resident owners of the property liable to taxation therefor, who shall also own a majority of the front feet owned by residents of the city abutting on the street or alley, proposed to be improved, have not filed with the city clerk a protest against such improvement, such finding and declaration shall be conclusive after the execution of the contract for said improvement, and no special tax bill shall be held invalid for the reason that a protest sufficiently signed was filed with the city clerk.