Dua (supplication) and depending upon Allah does not mean to leave working by what is possible.
The human makes dua to Allah that He facilitates his matter and in the same time he works to arrive to his objective and awaits help from Allah Subhana. And whoever awaits aid of Allah with honest intention and sincerity to Allah Subhana, he will surely find Divine help and aid present in front of him.
So there must be both things together, meaning that we work by what is possible (it is not correct that we leave what we can do) and in the same time we make dua and depend upon Allah.
{And for those who fear Allah,
He (ever) prepares a way out,
And He provides for him from (sources) he never could imagine.
And if any one puts his trust in Allah:
sufficient is (Allah) for him.
For Allah will surely accomplish his purpose: verily, for all things has Allah appointed a due proportion.} [Qur’an At-Talaq (65):2-3]
*Translation of Arabic text on the image:
In the name of Allah is its course and its anchorage.
بِسْمِ اللَّـهِ مَجْرَاهَا وَمُرْسَاهَا [Hud (11):41]