The authority is come from the Lord!

1 Kings 1:32-40
Solomon be anointed to a king of Israel by Zadok the priest, and Solomon rode the mule of David to Gihon.
Zodak the priest, Nathan the prophet, Benaiah son of Jehoiada and all the people shouted, "long live King Solomon!"
Gihon: A spring just outside the eastern wall of Jerusalem, in the Kidron Valley.
The tent: in which the Ark was kept.
And thanks to some quick thinking by the prophet Nathan, and even quicker action by the old king. Adonijah is out manoeuvred. Solomon is made king, initially co-regent with David.
Why?
David let Solomon be anointed in public place and people can see it, then people will know that Solomon is the king after him.
Solomon be a king is based on the power of God and the support of the people of Israel. So this king will be real king of Israel. The authority is come from the Lord.
How?
No rely on men or horse but rely on the Lord, Almighty!  Waiting for God's time and his way.