Step  1  :Isolate a square root on the left hand side :
     Original equationÂ
     4 = √-6-2x+√31-3x
     Isolate
     -√-6-2x = -4+√31-3x
     Tidy upÂ
     √-6-2x = 4-√31-3x
Step  2  :Eliminate the radical on the left hand side :
     Raise both sides to the second power
     (√-6-2x)2 = (4-√31-3x)2
     After squaringÂ
     -6-2x = 31-3x+16-8√31-3x
Step  3  :Get remaining radical by itself :
     Current equationÂ
     -6-2x = 31-3x+16-8√31-3x
     Isolate radical on the left hand side
     8√31-3x = 6+2x+31-3x+16
     Tidy upÂ
     8√31-3x = 53-x
Step  4  :Eliminate the radical on the left hand side :
     Raise both sides to the second power
     (8√31-3x)2 = (53-x)2
     After squaringÂ
     1984-192x = x2-106x+2809
Step  5  :Solve the quadratic equation :
     Rearranged equation
     x2  + 86x  + 825 = 0
     This equation has two rational roots:
      {x1, x2}={-11, -75}
Â
Step  6  :Check that the first solution is correct :
     Original equation, root isolated, after tidy up
     √-6-2x = 4-√31-3x
     Plug in  -11 for  xÂ
      √-6-2•(-11) = 4-√31-3•(-11)
      Simplify
      √16 = -4
      Solution does not checkÂ
      4 ≠ -4Â
Step  7  :Check that the second solution is correct :
     Original equation, root isolated, after tidy up
     √-6-2x = 4-√31-3x
     Plug in  -75 for  xÂ
      √-6-2•(-75) = 4-√31-3•(-75)
      Simplify
      √144 = -12
      Solution does not checkÂ
      12 ≠ -12Â
Hopefully this helped You