I am attaching the question image for the benefit of others. This is a tricky problem with infinite series.
To explain it , consider a simple equation without roots as shown below.
X = 1 + 1 + 1 + ......... (up to infinity)
Now you can call this X = 1 + X, because if you discard the first 1, you are still having 1 + 1 + ..... till infinity, which is again X as per the definition.
Infinity is basically something that is not countable. So you can say 1 subtracted from infinity = infinity, Or 1 added to Infinity is again Infinity.
I hope now the problem makes sense for you and how the equation became
X = Sqrt(2 + X). The reason is same as the above as in the 1 series.