Any amendment or amendments to this Constitution may be proposed in the Senate or House of Delegates, and if the same shall be agreed to by a majority of the members elected to each of the two houses, such proposed amendment or amendments shall be entered on their journals, the name of each member and how he voted to be recorded, and referred to the General Assembly at its first regular session held after the next general election of members of the House of Delegates. If at such regular session or any subsequent special session of that General Assembly the proposed amendment or amendments shall be agreed to by a majority of all the members elected to each house, then it shall be the duty of the General Assembly to submit such proposed amendment or amendments to the voters qualified to vote in elections by the people, in such manner as it shall prescribe and not sooner than ninety days after final passage by the General Assembly. If a majority of those voting vote in favor of any amendment, it shall become part of the Constitution on the date prescribed by the General Assembly in submitting the amendment to the voters.