6) \(\frac{x^2}{24}+\frac{x}{3}=\frac{x+9}{3}\)

Умножим обе части уравнения на \(24\):

\[x^2+8x=8(x+9)\]

\[x^2+8x=8x+72\]

\[x^2=72\]

\[x=\pm\sqrt{72}=\pm6\sqrt{2}\]

Ответ: \(x_1=-6\sqrt{2},\quad x_2=6\sqrt{2}\).