Whenever a majority of the inhabitants, qualified to vote for members of the Texas State Legislature, of any territory adjoining as said territory may be designated by the City Council or in case there are no such qualified voters in said territory, then when persons owning a majority of the land in area in said territory desire the annexation of such territory to Harker Heights, they may present a written petition to that effect to the City Council and shall attach to said petition the affidavit of one or more of their number to the effect that said petition is signed by majority of such qualified voters, or in case there are no such qualified voters said affidavit shall be to the effect that there are no such qualified voters in said territory and that the persons signing said petition own a majority of the land in area in said territory; and thereupon the City Council at regular session held not sooner than twenty days after the presentation of said petition may by ordinance annex such territory to Harker Heights, and thenceforth the said territory shall be a part of Harker Heights, and the inhabitants thereof, shall be entitled to all the rights and privileges of other citizens and shall be bound by the acts, ordinances, resolutions and regulations of said City.