Question 857779
{{{sqrt(3x+1)+2=sqrt(5x+9)}}}
Square both sides.
{{{(sqrt(3x+1)+2)(sqrt(3x+1)+2)=5x+9}}}
{{{(3x+1)+4sqrt(3x+1)+4=5x+9}}}
{{{4sqrt(3x+1)=5x+9-3x-1-4}}}
{{{4sqrt(3x+1)=2x+4}}}
{{{2sqrt(3x+1)=x+2}}}
Square both sides again.
{{{4(3x+1)=x^2+4x+4}}}
{{{12x+4=x^2+4x+4}}}
{{{x^2-8x=0}}}
{{{x(x-8)=0}}}
Two possible solutions:
{{{highlight(x=0)}}}
and 
{{{x-8=0}}}
{{{highlight(x=8)}}}
Make sure you go back and verify that these are actual solutions, a critical step for these type of problems.