\(4x^2+4x=27-10\sqrt{3}\)
\(\leftrightarrow4x^2+4x+1=25-10\sqrt{3}+3\)
\(\leftrightarrow\left(2x+1\right)^2=\left(5-\sqrt{3}\right)^2\)
\(\Rightarrow\left|2x+1\right|=5-\sqrt{3}\)
\(\leftrightarrow\left[{}\begin{matrix}2x+1=5-\sqrt{3}\\2x+1=\sqrt{3}-5\end{matrix}\right.\leftrightarrow\left[{}\begin{matrix}x=\dfrac{4-\sqrt{3}}{2}\\x=\dfrac{\sqrt{3}-6}{2}\end{matrix}\right.\)