Question 147845
The discriminant comes from the quadratic formula. It is what is under the root.
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 

This is for form ax^2+bx+c=f(x)
So, now just determine b^2-4ac given each equation.

9-4(-6)(2)=9+48=57. Because 57>0, we will have 2 real roots due to the quadratic formula's +/-.


Now for the second equation.
36. Because 36>0, we will have 2 real roots due to the quadratic formula's +/-.

I will tell you what happens in all other cases.

If discriminant<0 we will have 2 imaginary roots.
If discriminant=0 we will have 1 real root. These follow because of what happens with the root by definition.