Find $ain (0,1)$, $bin (1,infty)$ and $cin (2,infty)$ such that $a^2c+bleq 2a-1$


I am wondering if the solution set of the following problem exists in $mathbb{R}$.

Suppose $ain (0,1)$, $bin (1,infty)$ and $cin (2,infty)$ . Does a solution set of the below inequality exists? If yes, what is it? If no, what is the reason?

$$a^2c+bleq 2a-1.$$