Romans 9:14 to 9:24 and free will Do all Christians believe in predestination? If not, for those who don't, how do they explain Romans 9:14 - 9:24?

14 What shall we say then? There is no injustice with God, is there? May it never be! 15 For He says to Moses, “I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.” 16 So then it does not depend on the man who wills or the man who runs, but on God who has mercy. 17 For the Scripture says to Pharaoh, “For this very purpose I raised you up, to demonstrate My power in you, and that My name might be proclaimed throughout the whole earth.” 18 So then He has mercy on whom He desires, and He hardens whom He desires.
19 You will say to me then, “Why does He still find fault? For who resists His will?” 20 On the contrary, who are you, O man, who answers back to God? The thing molded will not say to the molder, “Why did you make me like this,” will it? 21 Or does not the potter have a right over the clay, to make from the same lump one vessel for honorable use and another for common use? 22 What if God, although willing to demonstrate His wrath and to make His power known, endured with much patience vessels of wrath prepared for destruction? 23 And He did so to make known the riches of His glory upon vessels of mercy, which He prepared beforehand for glory, 24 even us, whom He also called, not from among Jews only, but also from among Gentiles.

The passage says some are &quot;vessels of wrath prepared for destruction,&quot; and others are &quot;vessels of mercy, which He prepared beforehand for glory...&quot; Also when it says &quot;He hardens whom he desires,&quot; the implication is that when a person's heart becomes hardened, it is hardened by God in which case they did not do so of their free will. Both of these support the idea of predestination (the former more than the latter) and I want to know how a Christian who doesn't believe in predestination (or one who somehow harmonizes predestination and free will) would interpret this passage, particularly the things I mentioned.
Do all Christians believe in predestination?  No. 

Do all Christians
   believe in free-will?  No.

Does the Bible teach predestination? Yes

Does the Bible teach Free-Will?  Yes

Romans informs us that salvation is about God's choice.  Romans 10 informs of of man's responsibility to believe or man's choice.  Is Jesus God?  Yes.  Is Jesus Man?  Yes.  Coincidence that God operates in this way?