(1) By act of the General Assembly relating to one or more counties; or

(2) By authorization of the county boards of education under the following conditions:

(a) With the written approval of the Senator and the entire house legislative delegation from the county involved;

(b) Upon a written petition, signed by at least four fifths of the qualified electors embraced within the limits of each of the school districts involved, which shall state plainly to the county board of education the action petitioned and shall also bear the signed certificate of the members of the county board of registration that the number of electors who signed the petition represent at least four fifths of the qualified electors embraced within the limits of each of the school districts involved; or

(c) Upon the written petition, signed by at least one third of the qualified electors embraced within the limits of each of the school districts involved, which shall state primarily the action petitioned and shall bear the signed certificate of the members of the county board of registration that the number of the electors who signed the petition represent at least one third of the qualified electors embraced within the limits of each of the school districts involved; if such consolidation be approved favorably by a majority of the qualified electors of each of the school districts involved at an election called by the county board of education for the purpose.