\(\begin{array}{l}
A = 9{x^2} - 6x - 4 = {\left( {3x} \right)^2} - 2.3x.1 + 1 - 5\\
= {\left( {3x - 1} \right)^2} - 5\\
{\left( {3x - 1} \right)^2} \ge 0 \Rightarrow {\left( {3x - 1} \right)^2} - 5 \ge - 5 \Leftrightarrow A \ge - 5\\
\Rightarrow {A_{\min }} = - 5 \Leftrightarrow 3x - 1 = 0 \Leftrightarrow x = \frac{1}{3}
\end{array}\)
