What is the number of real solutions?
-7x²-11x-2=0

one solution?
two solutions?
no real solution?
cannot be determined

 [B]:  Two (2) real solutions .

Explanation:

  Given:   -7x² − 11x − 2 = 0 ;

    We see that it is in "quadratic format" ; that is:

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

   Multiply the entire equation by "-1" ; to get rid of the "negative number" :

             →   -1 * {-7x² − 11x − 2 = 0} ;
 
 to get:  →       7x²  + 11x + 2 = 0  ;

This expression is written in the "quadratic format"; 
 
                   ax² + bx + c = 0 ;  in which:  a = 7 ; b = 11; c = 2 ;

         The expression cannot be "factored"; so, we can solve for "x" ; by using the "quadratic equation formula" ;


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

Let us solve for:  "(2a)" :   2a = 2 * a = 2 * 7 = 14 ;

Let us solve for:  "(b² − 4ac)":  11² − 4*7*2 = 121 − 56 = 65; 
  
    →   √(b² − 4ac) = √65

    →   " -b" = -11 ;

So,   x = (-11 ± √65) / 14 ; 

There are TWO (2) solutions:

Solution 1)  x = (-11 + √65) / 14 = - 0.2098387322643893071;  AND:

Solution 2)  x = (-11 − √65) / 14 = -1.3615898391641821214 ;

So, there are TWO (2) real solutions.

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