[tex] \bf x^2-x=-\cfrac{1}{4}\implies \stackrel{\textit{multiplying by }\stackrel{LCD}{4}}{4x^2-4x=-1}\implies 4x^2-4x+1=0 [/tex]
[tex] \bf \qquad \qquad \qquad \textit{discriminant of a quadratic}
\\\\\\
\stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{-4}x\stackrel{\stackrel{c}{\downarrow }}{+1}
~~~~~~~~
\stackrel{discriminant}{b^2-4ac}=
\begin{cases}
\boxed{0}&\textit{one solution}\\
positive&\textit{two solutions}\\
negative&\textit{no solution}
\end{cases}
\\\\\\
(-4)^2-4(4)(1)\implies 16-16\implies \boxed{0} [/tex]
