### Instruction: Solve the inequality
\[-4x^2 + 7x + 2 < 0.\].### Response: The inequality factors as
\[-(4x + 1)(x - 2) < 0.\]Therefore, the solution is $x \in \boxed{\left( -\infty, -\frac{1}{4} \right) \cup (2,\infty)}.$. The answer is (-\infty,-\frac{1}{4})\cup(2,\infty)