The average of your tests is 77.667 and applying the weighting factor of 0.5 (50%) these are worth 38.83 toward your final grade (77.667•0.5 = 38.83)
The Exam 22/30 is 73.33% and applying the weighting factor of 0.05 (5%) it is worth 3.667 toward your final grade (73.333•0.05 = 3.667)
Your final score is "x" and applying the weighting factor of 0.25 (25%) it is worth 0.25x toward your final grade
Since you only have 80% of the possible score accounted for, you can take your desired 76 and multiply it by 0.80 (80%) to get the desired total of 60.8.
Adding these together gives:
38.83 + 3.67 + 0.25x = 60.8
0.25x = 60.8 - 38.83 - 3.67
0.25x = 18.3
x = 73.2
So you need a 73.2% on your final. Since the final is worth 150 points, you must get a score of 110/150 (which would actually give you a 73.3%).
If you get no partial credit of=n anything, it means you can miss 26 questions. If you did that, you would actually have a 74% for your final exam score.
But all that said, let me give you some advice, study as hard as you possibly can and try to get a 100% on your final. That is a much better plan.