Why ask God for solutions, according to Christianity?
Because God’s solutions are typically way better than only-human solutions. There is a harmony to them*, where things come together in a way that is typically beyond human engineering. (See satisfying endings to stories as an example, if unfamiliar with examples of this sort yourself.)
* (harmony is similar to the concept of wholeness, from which we get the term ‘holiness’ – holiness, not surprisingly, involves a kind of harmony)
So, it probably makes sense for a Christian to cultivate the habit of “God, help guide us to a solution on this.” I.e., the instinct should be to seek God’s guidance and coordination when encountering a problem. Whenever one finds oneself worrying about a problem, this is the habit to replace that thought pattern with. (This is an Iteration on “Thy will be done,” a part of the set of keys for Christian practice given by Jesus of Nazareth in the ‘Our Father’ in the Sermon on the Mount, supposedly.)
It is important to note that this isn’t about inaction (although non-action is an important component of any problem-solving tool-box – waiting for the correct circumstances, for example, before springing into action). Too often, it seems to me, Christians pray for God to ‘do something’, when an important point in Christianity is the Christians themselves doing things, guided by God.
Instead, the basic cycle is asking for guidance -> getting guidance -> acting on the guidance. This is part of the practice of ‘discernment’. If you don’t act (“Thy will be done“), then the cycle doesn’t complete.