\(x^2-3x+1=0\)

\(ax^2+bx+c=0\) is the standard form
\[x+\frac{1}{x}=3\]
Multiply both sides by \(x\): 
$$
\begin{aligned}
x^2+\frac{x}{x}&=3x\\
x^2+1&=3x\\
\therefore x^2-3x+1&=0
\end{aligned}
$$