Strictly dominant strategies $(s_i'')$ satisfy the condition: $$u_i(s_1,\dots,s_i',s_{i+1},\dots,s_n)<u_i(s_1,\dots,s_i'',s_{i+1},\dots,s_n)$$,where $u_i$ is the payoff of every strategy for player $i$ that can be formed from a strategy set $S_i$. In this case, for Firm I (representing the rows of the payoff matrix), a dominant strategy would exist if $50 > 20$ and $90+x > 140$ simultaneoulsy. For Firm II (representing the columns of the payoff matrix), a dominant strategy would exist if $160 > 140 $ and $50 > 90 - x$. Therefore the mutual solution would be: $$x\geq 50$$
As far as the Nash equilibrium is concerned, the only equilibrium possible is the set $(50,50)$ .