I see no reason to believe that Romans 9 has anything whatsoever to say on the matter of the predestination of individual persons to an ultimate destiny. This text is often appealed to in order to support the belief that God fore-ordains who gets saved. But this clearly does not honour context. This passage is Paul's full-dress treatment of how God has hardened Israel as part of His grand plan of redemption. It is a specifically historical argument about a particular thing God did in history - harden Israel. To generalize it beyond that it is to miss the very particular point that Paul is making - God hardened Israel to bring salvation to the Gentiles (Romans 11 hits you over the head with this).
At best, the only support this chapter might offer to the standard "predestination" position is that it establishes that, yes, God can be in the business of fore-ordaining the hardening of people. But that's about it - one needs to make a further case that God actually does predestine individuals.
Both Peter and Paul and Luke, included the concept of being foreordained to salvation
Romans 8, the amplified bible
29 For those whom He foreknew [of whom He was aware and loved beforehand], He also destined from the beginning [foreordaining them] to be molded into the image of His Son [and share inwardly His likeness], that He might become the firstborn among many brethren.
30 And those whom He thus foreordained, He also called; and those whom He called, He also justified (acquitted, made righteous, putting them into right standing with Himself). And those whom He justified, He also glorified [raising them to a heavenly dignity and condition or state of being].
1 Peter, an apostle (a special messenger) of Jesus Christ, [writing] to the elect exiles of the dispersion scattered (sowed) abroad in Pontus, Galatia, Cappadocia, Asia, and Bithynia,
2 Who were chosen
and foreknown by God the Father and consecrated (sanctified, made holy) by the Spirit to be obedient to Jesus Christ (the Messiah) and to be sprinkled with [His] blood: May grace (spiritual blessing) and peace be given you in increasing abundance [that spiritual peace to be realized in and through Christ, freedom from fears, agitating passions, and moral conflicts].
Acts 13
48 And when the Gentiles heard this, they rejoiced and glorified (praised and gave thanks for) the Word of God; and as many as were destined (appointed and ordained) to eternal life believed (adhered to, trusted in, and relied on Jesus as the Christ and their Savior).
Whole passage in context.
38 So let it be clearly known
and understood by you, brethren, that through this Man forgiveness
and removal of sins is now proclaimed to you;
39 And that through Him everyone who believes [who acknowledges Jesus as his Savior and devotes himself to Him] is absolved (cleared and freed) from every charge from which he could not be justified
and freed by the Law of Moses
and given right standing with God.
40 Take care, therefore, lest there come upon you what is spoken in the prophets:
41 Look, you scoffers
and scorners, and marvel and perish
and vanish away; for I am doing a deed in your days, a deed which you will never have confidence in
or believe, [even] if someone [clearly describing it in detail] declares it to you.the attainment through Christ of salvation in the kingdom of God].
45 But when the Jews saw the crowds, filled with envy
and jealousy they contradicted what was said by Paul and talked abusively [reviling and slandering him].
46 And Paul and Barnabas spoke out plainly
and boldly, saying, It was necessary that God’s message [concerning salvation through Christ] should be spoken to you first. But since you thrust it from you, you pass this judgment on yourselves that you are unworthy of eternal life
and out of your own mouth you will be judged. [Now] behold, we turn to the Gentiles (the heathen).
47 For so the Lord has charged us, saying, I have set you to be a light for the Gentiles (the heathen), that you may bring [eternal] salvation to the uttermost parts of the earth.
48 And when the Gentiles heard this, they rejoiced and glorified (praised and gave thanks for) the Word of God; and as many as were destined (appointed and ordained) to eternal life believed (adhered to, trusted in, and relied on Jesus as the Christ and their Savior).
49 And so the Word of the Lord [concerning eternal salvation through Christ] scattered
andspread throughout the whole region.