H(t)=16t^2+604 find how long it'll take to get the 348 feet

I believe you meant  - 16t^2 + 604 ft.  If you leave that - sign out, this function will never equal 348 feet.

-16t^2 + 604 = 348 can be solved:

-16t^2 = -256 ft, and t = 16 sec.  Whatever you are throwing will first rise, reach some max. value, and then begin falling, and eventually reach 348 ft.