\(-3x^2+5x-4=-\left(3x^2-5x+4\right)=-\left(3x^2-2\cdot\sqrt{3}\cdot\frac{5\sqrt{3}}{6}+\frac{25}{12}+\frac{23}{12}\right)\)
\(=-[\left(\sqrt{3}x-\frac{5\sqrt{3}}{6}\right)^2+\frac{23}{12}]< 0\)
Để bpt >0 thì
\(\left(m-4\right)x^2+\left(1+m\right)x+2m-1< 0\) (1)
\(\Delta=\left(m+1\right)^2-4\cdot\left(m-4\right)\cdot\left(2m-1\right)=-7m^2+38m-15\)
ĐK \(\left\{{}\begin{matrix}\Delta< 0\\a< 0\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}\left[{}\begin{matrix}m< \frac{19-\sqrt{466}}{7}\\m>\frac{19+\sqrt{466}}{7}\end{matrix}\right.\\m< 4\end{matrix}\right.\)
\(\Leftrightarrow m< \frac{19-\sqrt{466}}{7}\)
