[tex]\bf x^2=4x-5\implies x^2-4x+5=0\\\\
-------------------------------\\\\
\begin{array}{llccll}
& 1x^2& -4x& +5&=&0\\
&\uparrow &\uparrow &\uparrow \\
&a&b&c
\end{array}\qquad \qquad (-4)^2-4(1)(5)
\\\\\\
discriminant\implies b^2-4ac=
\begin{cases}
0&\textit{one solution}\\
positive&\textit{two solutions}\\
negative&\textit{no solution}
\end{cases}[/tex]
