Bhagvad Geeta Famous Quotes

One of my favorite quotes is as follows :

Its not very easy to interpret the philosophical meaning of these quote in today's materialistic world still lot of people have commented on this, I have been trying to analyze and understand this from a long time.

Does this mean "Do your deeds and don't worry about the results ?" or "Do your deeds and be detached form results " ? . One of the interpretation says
"
You have a right to perform your prescribed duty, but you are not entitled to the fruits of action। Never consider yourself the cause of the results of your activities, and never be attached to not doing your duty.

"
But How can a person not be worry about results of his/her deeds ? why a person should not be entitled to results ?

Even though I am not a Sanskrit scholar the most perfect version of interpretation I found ( IMHO ) is as follows.

"
Karmanye vadhikaraste
--you have the power to act only
ma phaleshu kadachna
--you do not have the power to influence the result
Karmaphalehtur bhurma te
--therefore you must act without the anticipation of the result
sangostvakarmani
--without succumbing to inaction
"

Please do let me know your thoughts