# 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?

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