Can you solve quadratic formula for 9x to the 2 power -144 equals 0?

Sure, you can (a = 9, b = 0, c = -144). However, in this case, since there is no linear term, it is easier to transfer the -144 to the right (9x2 = 144), then take the square root on both sides. Don't forget to add "plus or minus" before one of the terms, or you will miss one of the two solutions.