#### Answer

$x=2,3$

#### Work Step by Step

As per given question: $3x-5=(x-1)^2$
This can be written as: $3x-5=x^2-2x+1$
or, $x^2-2x+1-3x+5=0$
or, $x^2-5x+6=0$
Need to use factorization to solve the quadratic equation .
$x^2-2x-3x-6=0$
or, $(x-2)(x-3)=0$
This implies $x-2=0$ and $x-3=0$
Hence, $x=2,3$