Detachment is one of the most misunderstood ideas in the Gita. It is often taken as coldness or withdrawal. The Gita means something warmer and harder: caring fully while not clinging, acting fully while not demanding particular results, and enjoying life without being owned by it. It is a freedom of the heart, not an absence of love.
Gita 5.12 says that peace comes from relinquishing attachment to outcomes, while craving specific results leads to bondage and anxiety, and Gita 12.12 says renunciation of the fruits of action brings immediate peace. Gita 5.3 says a true renunciate is free from likes, dislikes, cravings and aversions, and Gita 18.2 distinguishes sannyasa, abandoning desire-driven actions, from tyaga, giving up attachment to the results of every action. Real renunciation is inner, not merely the cessation of activity.
The Gita offers practical supports. Gita 12.11 says that if full dedication seems out of reach, you can still act and let go of the fruits, using this to reduce pressure and worry. Gita 9.9 says the Lord remains free because He acts as an unattached witness, so fulfil your responsibilities fully while keeping your inner self unattached from outcomes. Gita 13.9 links detachment with honest reflection on life's limits, and Gita 15.3 asks for firm resolve in cutting the tree of attachment. Care deeply and hold lightly.