"Then King David said, 'Call in Bathsheba.' So she came into the king's presence and stood before him. The king then took an oath: 'As surely as the Lord lives, who has delivered me out of every trouble, I will surely carry out today what I swore to you by the Lord, the God of Israel: Solomon your son shall be king after me, and he will sit on my throne in my place.' Then Bathsheba bowed low with her face to the ground and, kneeling before the king said, 'May my lord King David live forever!'" NIV translation
The king came to his senses and restated his promise to Bathsheba that Solomon would be king.
"King David said, 'Call in Zadok the priest, Nathan the prophet and Benaliah son of Jehoiada.' When they came before the king, he said to them: 'Take your lord's servants with you and set Solomon my son on my own mule and take him down to Gihon. There have Zadok the priest and Nathan the prophet anoint him king over Israel. Blow the trumpet and shout, "Long live King Solomon!" Then you are to go up with him, and he is to come and sit on my throne and reign in my place. I have appointed him ruler over Israel and Judah.'" NIV translation
David backed up his promise with action as he ordered that they announce Solomon as the new king of Israel.
"Benaiah son of Jehoiada answered the king, 'Amen! May the Lord, the God of my lord the king, so declare it. As the Lord was with my lord the king, so may he be with Solomon to make his throne even greater than the throne of my lord King David!'" NIV translation
The military man pledged his loyalty to Solomon the son of David and asked a blessing upon him.
"So Zadok the priest, Nathan the prophet, Benaiah son of Jehoiada, the Kerethites and the Pelethites went down and put Solomon on King David's mule and escorted him to Gihon. Zadok the priest took the horn of oil from the sacred tent and anointed Solomon. Then they sounded the trumpet and all the people shouted, 'Long live King Solomon!' And all the people went up after him, playing flutes and rejoicing greatly, so that the ground shook with the sound." NIV translation
David's pick for king was made known as it was his own bodyguards that escorted them to Gihon. It was all done in the open so that the people could see and know that Solomon was the chosen king unlike Adonijah who had thrown a party for the upper class. This is a picture of the fact that Jesus, the King of Kings, was for all people and not just a select group of privileged people.