How do you solve #sqrt(2x+1/6)=x+5/6#?
I have taken you to a point where you can finish it off.
If you have a square root on one side of the equals and a 'non' square root on the other, you can 'get rid' of the root by squaring both sides. Giving:
Collecting terms on one side only of the equals to give us a quadratic equation.
I will let you finish this off.