Your starting equation is

    .      (1)


The domain is the set of all x, such that  3x + 2 >= 0,  i.e.  x > .


To solve the equation, notice that  0.04 = ;  so, equation (1) takes the form


     = ,   or

    
     = ,  which is the same as


     = .


The bases are the same in both sides of the equation;  hence, the indexes are the same


     = 


which implies


    sqrt(3x+2) = 2 + 2*3 = 8

    3x+2 = 8^2 = 64

    3x = 64 - 2 = 62

     x = .      ANSWER