Luke 15:18-19 is a good example of true repentance. This son did not claim any goodness of his own or try to justify his actions, but he humbled himself and appealed to the mercy of his father. We cannot approach God in self-righteousness, but we have to humble ourselves, put all of our faith in a Savior, and turn from our wicked ways (2 Chronicles 7:14). That is true repentance.

Repentance is a necessary part of salvation. Repentance may include godly sorrow, but sorrow does not always include repentance. Repentance is simply a change of mind accompanied by corresponding actions.

There is a godly type of sorrow and an ungodly type of sorrow. Godly sorrow leads to repentance. Ungodly sorrow, or the sorrow of this world, just kills.

Our culture has rejected all "negative" emotions. But God gave us the capacity for these negative emotions and there is a proper use of them.

People should feel bad about sin. There should be sorrow over our failures. This sorrow should lead to repentance, then when forgiveness is received, our sorrow should be cast upon the Lord (Isaiah 53:4).

The sorrow experienced by those who do not turn to God produces only death.

They grieve over their situation because they don't turn to God (that's repentance). Christians should only have sorrow until they repent. Once repentance has come, we need to appropriate the forgiveness and cleansing that are already ours through Christ (1 John 1:9). The positive change that our sorrows led us to, changes our attitude towards the things that caused us sorrow. 

Negatives become positives through Jesus.