Shaykh Yasir Qadhi talks about Allah's promise in answering dua. One of the most powerful verses in the Qur'an that ascertains the acceptability of any dua is as follows.
ادْعُونِي أَسْتَجِبْ لَكُمْ
Call on Me, I will answer your prayer.
[Surah Ghafir, 40:60]
There are three ways in which a dua is accepted.
You will get what you want
You will get something equivalent for the dua you asked
Any calamity that was in your way will be averted
The Shaykh implores us to never be stingy in asking duas to Allah. The more you ask Allah, the more He will love us.