[tex]\bf 2x^2=3x+5\implies 2x^2-3x-5=0
\\\\\\
\begin{array}{llccll}
&{{ 2}}x^2&{{ -3}}x&{{ -5}}&=0\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}
\\\\\\
discriminant\implies b^2-4ac=
\begin{cases}
0&\textit{one solution}\\
positive&\textit{two solutions}\\
negative&\textit{no solution}
\end{cases}\\\\
-------------------------------\\\\
(-3)^2-4(2)(-5)[/tex]
