6. Let $g(x)$ be a strictly increasing function defined for all $x \geq 0$. It is known that the range of $t$ satisfying
$$
\mathrm{g}\left(2 t^{2}+t+5\right)<\mathrm{g}\left(t^{2}-3 t+2\right)
$$
is $b<t<a$. Find $a-b$.