"Then the Jews sought Him at the feast, and said, 'Where is He?' And there was much complaining among the people concerning Him. Some said, 'He is good'; others said, 'No, on the contrary, He deceives the people.' However, no one spoke openly of Him for fear of the Jews. Now about the middle of the feast Jesus went up into the temple and taught. And the Jews marveled, saying, 'How does this Man know letters, having never studied?' Jesus answered them and said, 'My doctrine is not Mine, but His who sent Me. If anyone wills to do His will, he shall know concerning the doctrine, whether it is from God or whether I speak on My own authority. He who speaks from himself seeks his own glory; but He who seeks the glory of the One who sent Him is true, and no unrighteousness is in Him'" (John 7:11-18).
Jesus' fame and recent avoidance of Judea made His enemies (i.e., "the Jews", and more specifically, the religious leaders) anxious for Him to show Himself again in their midst. They expected Him to be at the feast and were looking for Him.
"There was much complaining among the people concerning Him" (John 7:12). It is possible there are several large groups talking and affirming various ideas about Jesus. There were those who favored Him and said that He was "good," and there were others who believed Him to be a deceiver in that He didn't teach and practice the traditions of the elders.
The murmuring among the people was on a restrained level and was not publicized in any way that would attract the attention of the Jewish leaders (cf. Matt. 10:32; Psa. 119:46). For a person to publicly speak favorably of Jesus was dangerous (e.g., John 9:22,34), yet the people were also reluctant to publicly speak out against Jesus just in case the views they express may become unpopular later with the religious leaders (cf. 7:26).
Although Jesus had come to the feast quietly, He now taught openly and boldly in the temple. Some believe that His sudden appearance fulfills a portion of Malachi 3:1.
The Jews were perplexed at Jesus' knowledge and understanding for they considered Him to be uneducated since He hadn't studied in the way they considered to be proper. He hadn't studied "letters"; in other words, He hadn't studied the written law and traditions in the great rabbinical schools in Jerusalem.
Sadly, similar attitudes persist today even within the church. If a Christian man preaches the whole counsel of God faithfully, and is longsuffering as he convinces, rebukes, and exhorts (cf. Acts 20:26,27; II Tim. 4:2), then he is qualified to preach, regardless of what school he has or hasn't gone to or what degrees he may or may not have earned. Consider this: If one's formal level of education is used as the determining factor for who can and cannot publicly preach the gospel, then none of the apostles--with the exception of Paul--would have ever been qualified!
Jesus explains in John 7:16 that He did not originate His teachings but that they were given by God the Father - "My doctrine is not Mine, but His who sent Me" (cf. 3:34). Let it be noted here that some mistakenly believe Jesus and the Father are identical and that there is no distinction whatsoever. Clearly this passage teaches otherwise, unless one is willing to conclude that Jesus is speaking nonsense or lying.
"If anyone wills to do His will, he shall know concerning the doctrine, whether it is from God or whether I speak on My own authority" (John 7:17). If a person has a strong determination (i.e., if he "wills") to do the Father's will, then he will know whether Jesus' teachings are divinely originated or manmade. When one is highly motivated to do what God has required, then his efforts will lead him to the truth that has been revealed from heaven (cf. Matt. 7:8). The problem with most of the Jews is that they didn't have honest hearts that were sincerely searching for the truth and seeking to do God's will. If they had been, then they would have easily been able to see that what Jesus taught was from God. Today, one who truly desires to do the will of God will never quibble at its requirements or question its validity but instead gladly submit to it completely.
A teacher who presents his own doctrine seeks to bring glory to himself (John 7:18). However, Jesus was not a teacher of this sort. He only taught that which the Father had authorized Him to teach. Thus, He didn't seek to exalt Himself but the Father, the One who sent Him. Because of this, Jesus' teachings are certainly true and He is righteous.