\(-6x^2+3x+4=0\)
\(\Leftrightarrow-6\left(x^2-\frac{x}{2}-\frac{2}{3}\right)=0\)
\(\Leftrightarrow x^2-2\cdot x\cdot\frac{1}{4}+\frac{1}{16}-\frac{35}{48}=0\)
\(\Leftrightarrow\left(x-\frac{1}{4}\right)^2=\left(\pm\sqrt{\frac{35}{48}}\right)^2\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\frac{1}{4}=\sqrt{\frac{35}{48}}\\x-\frac{1}{4}=-\sqrt{\frac{35}{48}}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{3+\sqrt{105}}{12}\\x=\frac{3-\sqrt{105}}{12}\end{matrix}\right.\)
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