Following the the property of an arithmetic sequence, we have :

\(\left(18x-3\right)-\left(17x+20\right)=\left(20x+1\right)-\left(18x-3\right)\)

\(\Leftrightarrow x-23=2x+4\Leftrightarrow2x-x=-23-4\Leftrightarrow x=-27\)

So, the answer is -27