#### Answer

$c=2,\dfrac{1}{5}$

#### Work Step by Step

Given: $f(c)=5c^2-11c+6$
Plug $f(c)=4$ then we have
$5c^2-11c+6=4$
This can be written as: $5c^2-11c+2=0$
Need to use factorization to solve the quadratic equation .
$5c^2-10c-c+2=0$
This implies $(c-2)(5c-1)=0$
Now, $c-2=0 $ and $5c-1=0$
Hence, $c=2,\dfrac{1}{5}$