\(5x^2+8x-4=0\)
\(\Rightarrow5\left(x^2+\dfrac{8}{5}x-\dfrac{4}{5}\right)=0\)
\(\Rightarrow x^2+\dfrac{8}{5}x-\dfrac{4}{5}=0\)
\(\Rightarrow x^2+2.x\dfrac{4}{5}+\dfrac{16}{25}-\dfrac{16}{25}-\dfrac{4}{5}=0\)
\(\Rightarrow\left(x+\dfrac{4}{5}\right)^2-\dfrac{36}{25}=0\)
\(\Rightarrow\left(x+\dfrac{4}{5}\right)^2=\dfrac{36}{25}\)
\(\Rightarrow\left[{}\begin{matrix}\left(x+\dfrac{4}{5}\right)^2=\left(\dfrac{6}{5}\right)^2\\\left(x+\dfrac{4}{5}\right)^2=\left(-\dfrac{6}{5}\right)^2\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x+\dfrac{4}{5}=\dfrac{6}{5}\\x+\dfrac{4}{5}=-\dfrac{6}{5}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{6}{5}-\dfrac{4}{5}\\x=-\dfrac{6}{5}-\dfrac{4}{5}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{2}{5}\\x=-2\end{matrix}\right.\)
