Answer:
x = 3 1/3
Explanation:
This is solved nicely using a graphing calculator. It shows the solution as x = 3 1/3.
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If you want to solve it by hand, you can square both sides of the equation. This gives ...
... 3x -1 +2√(3x -1) +1 = 3x +6
Subtracting 3x gives
... 2√(3x -1) = 6
... √(3x -1) = 3 . . . . . divide by 2
... 3x -1 = 9 . . . . . . . square both sides (again)
... 3x = 10 . . . . . . . . add 1
... x = 10/3 = 3 1/3 . . . . divide by 3
The solution is x = 3 1/3.
