2x^2-3x-9=0 can be factored as 1/2*(2x-6)*(2x+3)=0 so we can simplify and get (x-3)*(2x+3)=0

and so x= 3 or x= -3/2

The goal here is to solve for the unknown variable, x. That is, you want to find the value(s) of x the equation will equal to zero.

To solve for x, you have to factor the polynomial function to generate two binomials whose produce equals zero. Then, by the zero product property, we can set each binomial equal to zero and solve for x.

         2x² - 3x - 9 = 0

    (2x + 3)(x - 3) = 0

Set each binomial equal to zero:

      2x + 3 = 0                  and                 x - 3 = 0

            - 3     - 3                                         + 3     + 3

  ______________                               _______________

             2x = -3                                              x = 3

      (2x)/2 = (-3)/2

             x = -3/2

Thus,   2x² - 3x - 9 = 0   when   x = -3/2   and when   x = 3