Relation Between Values in a Cubic Function

Let the function $$ f $$ be defined as follows:

$$ f(x) = x^3 - 6x^2 + 9x $$

Suppose the function $$ g(x) $$ is defined as:

$$ g(x) = 2f(x) - 3 $$

If $$ g(a) = g(b) $$ for values $$ a $$ and $$ b $$ such that $$ a eq b $$, what is the relation between $$ a $$ and $$ b $$?