Romans 9:22 seems to say that God determines who is to be saved and who is to be damned.
This subject has seen a lot of controversy with many arguments on various sides. It would be impossible to answer the question to everyone’s satisfaction in this short paper. For those wishing an in-depth study I recommend the book Determined to Believe? by John C. Lennox. I can only make a few observations that might be helpful.
Romans 9:22-24 reads,
What if God, desiring to show his wrath and to make known his power, has endured with much patience vessels of wrath prepared for destruction, in order to make known the riches of his glory for vessels of mercy, which he has prepared beforehand for glory—even us whom he has called, not from the Jews only but also from the Gentiles?
First, notice that the verses quoted above begin with “What if”. It is not said that God actually desires what follows. This is an argument for the sovereignty of God. We will have to determine the significance of that. As to the desire of God, the most familiar verse in the Bible should answer that. “God sent his own Son.” (Jn. 3:16) “God is love” (1 Jn. 4:16) and “[love] does not seek its own” (1 Cor. 13:5, NASB) all testify to God’s desire that “all men be saved” (2 Pet. 3:9). Second, we are told that there are “vessels prepared for destruction.” It is easy to assume that God is the one who prepares them so, but that is not said. In fact, the uniform and persistent witness of Scripture is that men prepare themselves as vessels of wrath by their own rejection of the grace of God and their own wickedness. Some may be satisfied with these simple observations, but there is more we can learn from this passage of God’s great salvation.
This passage is far along in the subject of our salvation, so let’s go back to the foundational problem. In chapter 3 verses 9-20 the apostle summarizes the moral and spiritual ruin of man. Verse 10 reads, “no one understands; no one seeks for God.” So, it is emphasized that the condition of the unsaved person is such that he does not even “seek God.” The apostle John corroborates this profound ruin when he quotes the Lord Jesus “No one can come to me unless the Father who sent me draws him.” (Jn. 6:44) Notice He says, “no one can come to me.” Scripture uniformly declares the man is without hope and without strength. (E.g., Jer. 17:9)
Nevertheless, God still appeals to man: “Believe in the Lord Jesus, and you will be saved.” (Acts 16:31) The appeal to man is consistent throughout Scripture. This appeal cannot be vacuous. So, whatever the moral and spiritual ruin, there is something in man that can respond to God’s appeal. It seems that at the very least it must be the owning of one’s own ruined condition.
On God’s part, He is “willing to endure with much patience.” The word that should catch our attention is “endure.” This is not passive waiting. The pathos reflected in Matthew 23:37 is that of a heart that truly aches in sorrow over those who resist the gracious plea: “O Jerusalem, Jerusalem, the city that kills the prophets and stones those who are sent to it! How often would I have gathered your children together as a hen gathers her brood under her wings, and you would not!” The last phrase “you would not” must awaken every heart that could be awakened. But, if God is willing to endure, it is so that some might receive the eternal blessing of knowing “the riches of his glory.” (See Eph. 2:7)
 Some argue based on Matthew 21:33 that belief is dependent on repentance and on the basis of Ephesians 2:8 that even faith to believe is a “gift of God.” I prefer here to leave my statements vague and recommend the more detailed discussion in the book by John Lennox mentioned in the text.