\(HPT\Leftrightarrow\left\{{}\begin{matrix}\left(m+2\right)x+6x-9=4m-1\left(1\right)\\y=2x-3\end{matrix}\right.\\ \left(1\right)\Leftrightarrow x\left(m+8\right)=4m+8\\ \Leftrightarrow x=\dfrac{4m+8}{m+8}\Leftrightarrow A=\left(2x-3\right)^2+3x^2+8x=4x^2-12x+9+3x^2+8x\\ \Leftrightarrow A=7x^2-4x+9=7\left(x^2-2\cdot\dfrac{2}{7}x+\dfrac{9}{7}\right)\\ \Leftrightarrow A=7\left(x^2-\dfrac{4}{7}x+\dfrac{16}{49}+\dfrac{47}{49}\right)\\ \Leftrightarrow A=7\left(x-\dfrac{4}{7}\right)^2+\dfrac{47}{7}\ge\dfrac{47}{7}\\ A_{min}=\dfrac{47}{7}\Leftrightarrow x=\dfrac{4}{7}\Leftrightarrow\dfrac{4m+8}{m+8}=\dfrac{4}{7}\)
Từ đó bạn giải được \(m=-1\)
