In the constitution what was the solution the framers devised to counteract their mistrust of the general public?

There were two solutions. One has been discarded by the 17th Amendment and one still survives today. The first was the provision in Article 1, Section 3, Clause 1 of the Constitution, which provided that Senators be chosen by the state legislatures rather than by the popular vote. The 17th Amendment changed that to have Senators chosen by popular vote just the way Representatives are. The second was using the Electoral College as the true vote for President. Article 2, Section 1, Clause 2 of the US Constitution provides for the appointment of Electors in each state. Each state is entitled to a number of electors that equals the total amount of Representatives and Senators the state is entitled to have. Each political party running a candidate in an election has its own set of potential electors. If one political party's candidate wins the general vote, then that set of potential electors become the Electors for that state. The Framers devised this as a way of insulating the choice of President from irresponsible voters choosing a President who would threaten their property and businesses in favor of persons with no property. It was expected that the Electors would be wealthy people and if it appeared that a President who would threaten their wealth was elected by popular vote, the Electors were free, and still are today, to vote for another more acceptable candidate.