Question

How was the conflict surrounding the election of 1824 finally settled

Answer 1

Since there was no way to decide who would be the next president, the house of representatives had a vote in which they voted for John Quincy Adams to become the next president of the US.

Answer 2

The answer is: A majority vote in the House of Representatives.

Eventually, the vote in the house of representatives vote for the election of John Quincy Adams.  From the 24  state delegates that held the position within the house of representatives, John Quincy Adams received 13 of the votes, while Jackson and Crawford only receive 7 and 4 respectively.