Answer
No real solution
Work Step by Step
Given \begin{equation}
4 x^2-6 x+20=0.
\end{equation} Apply the method of completing the square to solve for $x$. Make sure that the coefficient of the square term is one before adding half the square of the coefficient of the $x$ term to both sides. First divide each side by $4$: \begin{equation}
\begin{aligned}
\frac{4 x^2-6 x+20}{4} & =\frac{0}{4} \\
x^2-1.5 x+5 & =0 \\
x^2-1.5x&=-5\\
x^2-2\cdot 0.75 x+0.75^2 & =-5+0.75^2 \\
(x-0.75)^2 & =-4.4375
\end{aligned}
\end{equation} We got that $(x-0.75)^2<0$, hence there is no real solution.
