Đặt \(x^2-4x=t\)
\(\Rightarrow t^2-8t+15=0\)
\(\Leftrightarrow t^2-3t-5t+15=0\)
\(\Leftrightarrow t\left(t-3\right)-5\left(t-3\right)=0\)
\(\Leftrightarrow\left(t-3\right)\left(t-5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}t=5\\t=3\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x^2-4x=5\\x^2-4x=3\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2-4x-5=0\\x^2-4x-3=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x^2+x-5x-5=0\\x^2-4x+4-7=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x\left(x+1\right)-5\left(x+1\right)=0\\\left(x-2\right)^2-7=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x+1\right)\left(x-5\right)=0\\\left(x-2-\sqrt{7}\right)\left(x-2+\sqrt{7}\right)=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=5\\x=2+\sqrt{7}\\x=2-\sqrt{7}\end{matrix}\right.\)