Answer
Choice C;
should be solved using the Quadratic Formula
Work Step by Step
The discriminant of a quadratic equation $ax^2+bx+c=0,$ is given by $b^2-4ac$. Thus, the discriminant of the given equation, $
9x^2-12x-1
,$ is
\begin{align*}\require{cancel}
&
(-12)^2-4(9)(-1)
\\&=
144+36
\\&=
180
.\end{align*}
Since the discriminant is positive and is a non-perfect square, then the equation $
9x^2-12x-1
$ has two irrational numbers as solutions or $\text{
Choice C
}$.
Furthermore, since the discriminant is a non-perfect square, then the given equation CANNOT be solved using the Zero-Factor Property. Hence, the Quadratic Formula should be used.