Please solve this radical equation. Show all your steps and explain thoroughly what you did. Thank you for your time and help.

Here's my steps, in gory detail:

1) Isolate the radical on one side of the equation
2) Square both sides to get rid of the radical
3) Collect up like terms into the form :a*x^2 + b*x + c = 0
4) Factor the thing (or use the quadratic formula for steps 4 and 5 if you prefer)
5) Set each of the factors to 0 and solve for your two roots ("solve" being kind of overstated, here)
6) Check the answers just to be sure they aren't extraneous (in this case they are both valid, but it's good practice to check when you do the "square both sides" thing).

sqrt(x-3) = x-3
sqrt(y) = y only if y = 0 or y = 1 so we need
x-3 = 0 or x-3 = 1 hence x = 3 or x = 4

Have not needed it since school, I was lied to and told I would need it the rest of me life. Good thing I didnt pay attention.

X-3=(X-3)^2
So, X-3 = 1
So, X=4

That’s cheating. You should do your own homework.

Young show-off! It's been 30 years since I took algebra!

Well x = 3

Sqrt (3-3)=0
0+3 = 3

4