Is God too busy to swoop up your cares and handle them? Is He unconcerned about what concerns you? If God were truly indifferent to your worries, wouldn't that give you ample support to be indifferent about them as well? At any rate the Word of our Lord declares differently; a simple command is given to those who wish to obey Him and the reward is great.
Cast your cares on the LORD
and he will sustain you;
he will never let the righteous fall. (psalm 55:2)
This is a step of obedience; to let Him in on what troubles your heart, however great or small or wicked or frightening. As if He doesn't already know, the love of God waits for an honest answer from us so He can demonstrate the peace He desires to give in an intimate sort of way. The immanence of God will shock you, the greatness of God will bring tranquility to your soul. Oswald Chambers says somewhere that we ought not to count any cost before we place God in the equation. I need to let that settle more in my thinking, because when it does I am unshakeable. Break the fear down and place God (whose name is revealed as PEACE in Judges 6:24) on every level. Hook your detailed care onto the end of a fishing line and cast it into the solar system. God is bigger than that, and no bait is needed.
And for those of you who are like me, who go searching for the worry after we've already got rid of it, faithfully keep on casting it back onto the Lord. Once you have given it to Him, it is in His court. It is now His responsibility to worry about.