(2x-5)²=9
⇔(2x-5)(2x-5)=9
⇔4x²-10x-10x+25=9
⇔4x²-20x+25-9=0
⇔4x²-20x+16=0
⇔(4x²-4x)-(16x-16)=0
⇔4x(x-1)-16(x-1)=0
⇔(x-1)(4x-16)=0
⇔4(x-1)(x-4)=0
⇔\(\left[ \begin{array}{l}x-1=0\\x-4=0\end{array} \right.\)⇔\(\left[ \begin{array}{l}x=0+1\\x=0+4\end{array} \right.\)⇔\(\left[ \begin{array}{l}x=1\\x=4\end{array} \right.\)
Vậy x=1 hoặc x=4.