[tex]\displaystyle\\
2x^2-3x+2\ \textless \ 1\\\\
2x^2-3x+2-1\ \textless \ 0\\\\
2x^2-3x+1\ \textless \ 0\\\\
\text{Ecuatia atasata acestei inecuatii este:}\\
2x^2-3x+1=0\\\\
\text{Functia atasata inecuatiei este:}\\
f(x)=2x^2-3x+1\\\\
\text{Rezolvam ecuatia.}\\\\
x_{12}=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{3\pm\sqrt{9-8}}{4}=\frac{3\pm1}{4}\\\\
x_1=\frac{3-1}{4}=\frac{2}{4}=\boxed{\frac{1}{2}}\\\\
x_2=\frac{3+1}{4}=\frac{4}{4}=\boxed{1}\\\\
\text{Coeficientul lui }x^2 \text{ este pozitiv. } 2\ \textgreater \ 0[/tex]
[tex]\displaystyle\\
\Longrightarrow~~~\text{Functia este pozitiva in afara radacinilor si negativa intre ele.} \\\\
\Longrightarrow~~~\boxed{x \in \left( \frac{1}{2};~1 \right)}[/tex]
