\(A=\dfrac{-22x^2-5x+6}{3x^2}=-\dfrac{22}{3}-\dfrac{5}{3x}+\dfrac{2}{x^2}\)
\(=\dfrac{2}{x^2}-\dfrac{5}{3x}+\dfrac{25}{72}-\dfrac{553}{72}\)
\(=\left(\dfrac{\sqrt{2}}{x}-\dfrac{5\sqrt{2}}{12}\right)^2-\dfrac{553}{72}\ge\dfrac{-553}{72}\)
Đẳng thức xảy ra \(\Leftrightarrow\left(\dfrac{\sqrt{2}}{x}-\dfrac{5\sqrt{2}}{12}\right)^2=0\Leftrightarrow x=\dfrac{12}{5}\)