1+x=√1+5x

If the whole expression  1 + 5x  is under the square root sign:

          1 + x  =  √(1 + 5x)

Remove the square root sign by squaring both sides:

          ( 1 + x )²  =  ( √(1 + 5x )²

      1 + 2x + x²   =   1 + 5x

Subtract 1 + 5x from both sides and rearranging:

              x² - 3x  =  0

        x ( x - 3 )  =  0

So  x = 0  or  x = 3

But these are only possibilities! They must be checked!

         1 + 0  =  √(1 + 5·0)     --->   1  =  √1      Yes!

         1 + 3  =  √(1 + 5·3)      --->  4  =  √(16)  =  4     Yes!

So, both  0  and  3  work.

1 + x = √(1 + 5x)   square both sides

1 + 2x + x ^2   = 1 + 5x     subtract 1 + 5x from both sides

-3x + x^2  = 0     rearrange

x^2 - 3x = 0        factor

x (x - 3)     and setting each factor to 0, we get that  x = 3  or x = 0

Make sure to check these answers....square root equations of this sort often give "extraneous" answers  that will not work in the original problem......here, we're OK though !!!