You are allowed to use any valid way of finding the correct answer.
If you do 4Unit, can I recommend you do it that way (from first principles) and create your equations for each specific situation. Not a lot of thought needed to do them, then.
find the time taken to reach max height.... find max hieght and then pretentend the object was launced from that height (ie coz v=0) as all objects accelerate at the same rate on earth.
then add the two times together and there youre time of flight, even when the object was projected from a height..... and hey presto u dont have to use the quadraatic formula...