[tex]\bf \qquad \qquad \qquad \textit{discriminant of a quadratic}
\\\\\\
0=\stackrel{\stackrel{a}{\downarrow }}{-2}x^2\stackrel{\stackrel{b}{\downarrow }}{-3}x\stackrel{\stackrel{c}{\downarrow }}{+8}
~~~~~~~~
\stackrel{discriminant}{b^2-4ac}=
\begin{cases}
0&\textit{one solution}\\
positive&\textit{two solutions}\\
negative&\textit{no solution}
\end{cases}
\\\\\\
(-3)^2-4(-2)(8)\implies 9+64\implies 73[/tex]
notice, is positive.
