[tex](m-3)x^2-2(3m-4)x+7m-6<0\\ \\Conditii:~m-3<0 \Rightarrow~m<3 \Rightarrow m\in (-oo;~3)~(Graficul~functiei~sa~aibe~ramurile~in~jos)~\\ \\si~\Delta<0~(sa~nu~intersecteze~axa~Ox):\\ \\ \Delta=[-2(3m-4)]^2-4(m-3)(7m-6)=\\ \\=4(3m-4)^2-4(7m^2-6m-21m+18)=\\ \\=4(9m^2-24m+16)-28m^2+108m-72=\\ \\=36m^2-96m+64-28m^2+108m-72\\ \\ \Delta=8m^2+12m-8\\ \\ \Delta<0 \Rightarrow 8m^2+12m-8<0~|:4\\ \\ 2m^2+3m-2<0\\ \\ Observam~ca~2>0~(coeficientul~lui~m^2) \Rightarrow functia~are~valori~negative~pe~intervalul~(m_1;~m_2)\\ \\ \Delta_m=3^2-4\cdot2\cdot(-2)=9+16=25 \Rightarrow \sqrt{\Delta_m}=5\\ \\ m_{1;2}=\frac{-3\pm5}{2\cdot2}\\ \\ \Rightarrow m_1=\frac{2}{4}=\frac{1}{2}~si~ m_2=\frac{-8}{4}=-2\\ \\ Deci~\Delta<0~cand~m\in(-2;~\frac{1}{2})\\ \\ Facem~intersectia:~(-2;~\frac{1}{2})n(-oo;~3)=(-2;~\frac{1}{2}) \Rightarrow \boxed{m\in(-2;~\frac{1}{2})}[/tex]
