The city council of the City of Monahans may from time to time, after hearing and public notice of such hearing given by one (1) publication in the official newspaper at least fifteen (15) days before the time of hearing, amend, supplement or change the regulations and districts herein or subsequently established. Whenever the owner of fifty (50) percent or more of the area of all the property within a radius of two hundred (200) feet of any area proposed to be changed shall present to the council a petition duly signed and acknowledged by them, requesting any such amendment, supplement or change of the regulations prescribed for such district, or part thereof, the council shall act upon such petition within ninety (90) days after the filing thereof. In case, however, of a protest against a change, signed by the owners of twenty (20) percent or more either of the area of the lots included in proposed change, or of those immediately adjacent in the rear thereof extending two hundred (200) feet therefrom, or of those directly opposite thereto extending two hundred (200) feet from the street frontage of such opposite lots, such amendment shall not become effective except by a favorable vote of three-fourths (3/4) of the voting members of the city council. In all cases where any person or persons shall petition the council to amend this article or the map, such person or persons shall bear all expense of the publication of the required notice of the required public hearing.