Isolate one radical term on one side:

                   = 

                 = 


     - 8 + 16 = 2x - 10

    3x + 1 - 8 + 16 = 2x - 10

        3x - 8 + 17 = 2x - 10

Isolate the radical term on one side:

                  x + 27 = 8

Square both sides:

               (x + 27)² = 8²

          x² + 54x + 729 = 64(3x + 1)

          x² + 54x + 729 = 192x + 64

Get 0 on the right:

         x² - 138x + 665 = 0         

Factor:

        (x - 5)(x - 133) = 0

Use the zero factor principle:

    x - 5 = 0        x - 133 = 0 
        x = 5              x = 133

We much check all solution because squaring both sides
often but not always introduces extraneous answers.

Checking x = 5 in the original:





4 - 0 = 4
    4 = 4

So x = 5 is a solution.

Checking x = 133 in the original:





20 - 16 = 4
      4 = 4

So x = 133 is also a solution.

Edwin