This means that you answers are restricted two ways:
1. 6x+2>=0, so 6x>=-2, x>=2/6, x>=1/3
2. x-1>=0, so x>=1
BOTH must hold, so we combine them: x>=1.
Whatever "solutions" you may find, they MUST be >= 1.
Now square everything in sight:
(x-1)² = 6x+2
Work out the brackets
Everything to the left side of the =-sign
Factorize, or use abc-formula
Check the solutions! Only if they are >= 1 they are really solutions.
Reason for this nitpicking: by squaring everything, you lose the information about the square root and you could get fake solutions...