I will continue from 3x^2 - 48x + 242, which is what you got.
3x^2 - 48x + 242
= (3x^2 - 48x) + 242
= 3(x^2 - 16x) + 242
= 3(x - 8)^2 - 3(64) + 242
= 3(x - 8)^2 - 192 + 242
= 3(x - 8)^2 + 50
Notice that 3(x - 8)^2 >= 0 for all real values of x.
Hence, the value of x which will result in the minimum value of 3(x - 8)^2 + 50 will be x = 8.