$${R_{net}} = {{ma} \over 3} + {a \over {2m}}$$

$$ = a\left[ {{m \over 3} + {1 \over {2m}} - {2 \over {\sqrt 6 }} + {2 \over {\sqrt 6 }}} \right]$$

$$ = a\left[ {{{\left( {\sqrt {{m \over 3}} - {1 \over {\sqrt {2m} }}} \right)}^2} + \sqrt {{2 \over 3}} } \right]$$

This will be minimum when

$$\sqrt {{m \over 3}} = {1 \over {\sqrt {2m} }}$$

or $$m = \sqrt {{3 \over 2}} $$

so $$x = 3$$