What is the number of real solutions?
-8x²=8x-9
1?
2?
no real solution?
cannot be determined.

The answer is:  [B]:  "2 (two) real solutions" .

Explanation:

Given:  -8x² = 8x − 9 ;  

Let us write this equation in "quadratic format";  that is:

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

   So, given:  -8x² = 8x − 9 ; 
 
Let us subtract "8x"; and add "9"; to EACH SIDE of the equation;

                     -8x² − 8x + 9 = 8x − 9 − 8x + 9 ;

 to get:         -8x² − 8x + 9 = 0 ;

Now, let's multiply the ENTIRE equation (both sides); by "-1", to get rid of the "negative" sign ;

                -1 * { -8x² − 8x + 9 = 0} ;

 to get:   →  8x² + 8x − 9 = 0 ;
 
               This equation is in "quadratic format", which is:
    " ax² + bx + c = 0 " ; in which:  a = 8; b = 8; and c = -9 ;

This can be solved by using the "quadratic equation formula" :

            x = {-b ± √(b² − 4ac)}  / {2a} ;  

First, let us solve for "2a", that is: "2 * a" ; (the "denominator") ;
 
                                 → (2a) = (2*a) = (2*8) = 16 .

Then, let us solve for:  "b² − 4ac" ;  
           
     → 8² − (4*8*-9) = 64 − (-288) = 64 + 288 = 352 ;

Then, let us solve for:  " √(b² − 4ac)"

= √(352) = 18.7616630392937182

Then, " - b " = "-8" .

  x = (-8 ± 18.7616630392937182) / 16 ; 

So, we have TWO (2) solutions:

1) x = (-8 + 18.7616630392937182) / 16 = 0.6726039399558573875

and: 

2) x = (-8 − 18.7616630392937182) / 16 = -1.6726039399558573875 ;

which are real solutions.

The answer is:  [B]:  "2 real solutions" .

-8x²=8x-9

-8x² -8x +9 = 0

The solutions are:
-1.6726 and
0.6726

Both are real numbers