Question 1402
{{{sqrt(5x+1)+2=2x}}}
You'll first want to subtract 2 from both sides of the equation so as to isolate the square root.

{{{sqrt(5x+1)=2x-2}}}

Next, square both sides to eliminate the square root.

{{{sqrt(5x+1)^2=(2x-2)^2}}}
{{{5x+1=(2x-2)(2x-2)}}}
{{{5x+1=4x^2-8x+4}}}

You'll next want to move all of your terms to one side of the equation. Do this by subtracting 5x and 1 from both sides.

{{{5x+1-5x-1=4x^2-8x+4-5x-1}}}

Combine like terms to get {{{0=4x^2-13x+3}}}.  This quadratic can be factored into {{{(4x-1)(x-3)=0}}}.  So either {{{4x-1=0}}} or {{{x-3=0}}}. After solving both equations, you'll get that x=(1/4) or 3.

To check your answers, plug both (1/4) and 3 back into the original problem. Checking 3 first, we see that {{{sqrt(5(3)+1)+2=sqrt(16)+2=4+2=6}}} Notice that this is equivalent to the other side of the equation {{{2*3=6}}}.  So this answer checks.

But notice that (1/4) does not check when you plug it back into the original problem:  {{{sqrt(5(1/4)+1)+2=sqrt(9/4)+2=(3/2)+2=(7/2)}}} and the other side of the equation gives us that {{{2(1/4)=(1/2)}}}.  

That means that this equation has only one solution x=3.

(I didn't see the other solution that looks just like this, so sorry for the redundancy.  I only saw the first incomplete solution. =) )