It means EITHER

     x^2 - 20x - 1 = 20

OR

     x^2 - 20x - 1 = -20.


Case 1) :   x^2 - 20x - 1 = 20.


     Then  x^2 - 20x - 21 = 0.

     Factor left side  (x-20)*(x+1) = 0

     giving the roots  x= 20  and  x= -1.



Case 2) :   x^2 - 20x - 1 = -20.


     Then  x^2 - 20x + 19 = 0.

     Factor left side  (x-19)*(x-1) = 0

     giving the roots  x= 19  and  x= 1.


ANSWER.  There are 4 solutions  x= -1, 1, 19 and 20.

Plot y = |x^2 - 20x - 1| (red)  and  y = 20 (green)