a)
[tex]\it x^2-3x=54 \Rightarrow x^2-3x-54=0 \Rightarrow x^2-9x+6x-45=0 \Rightarrow \\ \\ \Rightarrow x(x-9)+6(x-9)=0 \Rightarrow (x-9)(x+6)=0\begin{cases}\it x+6=0 \Rightarrow x_1=-6\\ \\ \it x-9\ =0 \Rightarrow \ x_2=9\end{cases}[/tex]
b)
[tex]\it x+\dfrac{2}{x}=\dfrac{17}{6}\Big|_{\cdot6x} \Rightarrow 6x^2+12=17x \Rightarrow 6x^2-17x+12=0 \Rightarrow \\ \\ \\ \Rightarrow 6x^2-9x-8x+12=0 \Rightarrow 6x(x-1,5)-8(x-1,5)=0 \Rightarrow \\ \\ \Rightarrow (x-1,5)(6x-8)=0 \Rightarrow \begin{cases}\it x-1,5=0 \Rightarrow x=1,5=\dfrac{3}{2}\\ \\ \\ \it 6x-8=0 \Rightarrow x=\dfrac{\ 8^{(2}}{6}=\dfrac{4}{3} \end{cases}[/tex]
