What is the solution set of the quadratic inequality 6x^2 + 1 is less or equal to zero

There are no solutions to that inequality.

Step-by-step explanation:

Without actually doing any operations on the inequality, just by giving it a good look: you will see that there no way, for any x, negative or positive, that the expression will become negative or zero. x^2 is always non-negative, and the + 1 bias ensures the expression will never ever, like, n-e-v-e-r, be anything but positive.