The answer lies with the biblical definition of repentance. Most of us know repentance as a turning from sin. This is a partial understanding of biblical repentance. Biblical repentance is truly a gift, it shows up with the exercise of faith.
Acts 5:31 (KJV)
31 Him hath God exalted with his right hand to be a Prince and a Saviour, for to give repentance to Israel, and forgiveness of sins.
Acts 11:18 (KJV)
When they heard these things, they held their peace, and glorified God, saying, Then hath God also to the Gentiles granted repentance unto life.
2 Timothy 2:25 (KJV)
25 In meekness instructing those that oppose themselves; if God peradventure will give them repentance to the acknowledging of the truth;
The gift of repentance is symbolized by baptism. John the Baptist did not preach “repent” for the forgiveness of sins; he preached the “baptism of repentance for the remission of sins”. You do not baptize yourself; in baptism something comes upon you. This is the picture of the Holy Spirit.
John did baptize in the wilderness, and preach the baptism of repentance for the remission of sins.
And he came into all the country about Jordan, preaching the baptism of repentance for the remission of sins;
In Acts 19:4, Paul defines the term, “baptism of repentance” as believing in the Lord Jesus Christ.
Then said Paul, John verily baptized with the baptism of repentance, saying unto the people, that they should believe on him which should come after him, that is, on Christ Jesus.
So in Acts 17:30, Paul is consistent in his definition of repentance. He tells the Greeks that God wants all men to believe on the Lord Jesus Christ.
Charles P. Bayliss of Dallas Theological Seminary published a great article in the Michigan Theological Journal entitled REPENTANCE IN ACTS IN LIGHT OF DEUTERONOMY 30, explains that repentance is a “return” to a covenant relationship with God where God does all the work and we are just recipients of His grace. He cites Deuteronomy 30:6 as the place where God introduces the new covenant where God would “return” Israel to Himself and God alone would circumcise the heart of Israel. Dr Bayliss talking about Deuteronomy 30:6:
“The phrase ‘the LORD your God will circumcise your heart’
introduced the New Covenant. The New Covenant was a change
which God would enact within man, as opposed to a change which
man would accomplish on his own.* Ezekiel 36 and Jeremiah 31
expanded Deuteronomy 30:6 further.
Thus Moses' final sermon to the nation prophesied a time
when Israel would return to covenant relationship, and God would
change their hearts. It was one of the earliest, most specific
references to the New Covenant. It is this return that is called
Here is Dr Bayliss talking about the difference between Peter’s first sermon in Acts 2 where he tells his Jewish audience to repent and “return” verses Peter’s second sermon in Acts 10 where he instructs the Gentiles just to believe.
“The first several chapters of Acts explain the reception of the
New Covenant by a remnant of the nation Israel. Chapter 10
explains the inclusion of Gentiles into that promise. If "repentance"
was a return to covenant relationship, then how was it that Gentiles
might return according to Deuteronomy 30:1-6, when they never
had a covenant relationship to which to return? It is one of the major
purposes of Acts to explain the inclusion of Gentiles in the New
Dr. Baylis cites Acts 10, where Peter has gone to the home of Cornelius for the purpose of explaining the Gospel message to the Gentiles.
“This message was absent of any accusations of killing the Messiah, since it was the Jews that had done this. It is also absent of any mention of the word "repentance" since Deuteronomy 30 was addressed only to Israel, and would have meant nothing to Cornelius as a Gentile. However, other than the substitution of the word "believe" for "repent," the elements are the same. Belief brought forth forgiveness of sins and the gift of the Holy Spirit (10:44-45), the elements of the New Covenant. The sign of the New Covenant, baptism, was then administered to these Gentiles in 10:47.”8