Question 464614
Transpose x to the right side:

{{{sqrt(3x + 1) = 13 - x}}}

Square both sides:

{{{3x+1 = (13 - x)^2 = 169 - 29x + x^2}}}

<==> {{{0 = 168 - 29x + x^2}}}

<==> 0 = (21 - x)(8 - x)  ==> x = 21, 8.

x = 21 is not a solution, because 21 > 13, and {{{sqrt(3x + 1) >= 0}}}.

x = 8 satisfies the equation, and thus is the final answer.