What is the number of real solutions?
-11x²-10x=-1

1?
2?
no real solution?
cannot be determined

 [B]:  There are "2" (two) real solutions.

Explanation:

Given:    -11x² − 10x = -1 ; 

Let us see if we can write this in "quadratic format" ; that is:

              ax² + bx + c = 0 ; a ≠ 0 ;


So, given:  -11x² − 10x = -1  ;  

Add "1" to EACH side of the equation;

               -11x² − 10x + 1 = -1 + 1 ; 

to get:     -11x² − 10x + 1 = 0 ;

Now, let us multiply the ENTIRE equation by "-1";
                            to get rid of the "negative sign" ;

                -1 * { -11x² − 10x + 1 = 0 } ; 

                         11x²  + 10x − 1 = 0 ;

This equation is written in quadratic format:

             " ax² + bx + c = 0 " ; in which:  a = 11 ;  b = 10 ; c = -1 ;

 Can the equation:  " 11x²  + 10x − 1 = 0 " ; be factored?  Yes! ;

                           →    (x + 1) (11x − 1) = 0 ;  There are two solutions; 
the equation holds true when EITHER of the TWO MULTIPLICANDS ; or both of them, are equal to "0"; since anything multiplied by "0" equals "0" .

        So,  (x + 1) = 0 ; 
 Subtract "1" from each side of the equation;
                x + 1 − 1 = 0 − 1 ; 
 to get:         x = -1

       So, 11x − 1 = 0 ;
Add "1" to each side of the equation;
              11x − 1 + 1 = 0 + 1 ;
to get:          11x = 1 ;

Divide EACH side of the equation by "11"; to isolate "x" on one side of the equation; and to solve for "x" ;

                    11x/11 = 1/11;   x = 1/11 = 0.0909090909090909

So, yes; there are 2 (two) real solutions.