If you have the quadratic equation [tex]ax^2 + bx + c=0[/tex], its discriminant is
[tex]b^2 - 4ac[/tex]
Now, your equation is [tex]-2x^2 + 3[/tex], so we have [tex]a=-2[/tex] , [tex]b=0[/tex] (because the quoeficient of [tex]x[/tex] in your equation is 0) and [tex]c=3[/tex].
Therfore the discriminant of your equation is:
[tex]b^2 - 4ac=(0)^2 - 4(-2)(3)=24[/tex]
That is positive.
When you have a positive discriminant, it means that your equation has two distinct real number solutions.
When this is negative you don't have any real number solution, and when is zero you have only one solution.
