Giải phương trình: \(2{x^2} - 2x - 3 = 0\).

\(2{x^2} - 2x - 3 = 0 \Leftrightarrow {x^2} - x - \frac{3}{2} = 0\)

\( \Leftrightarrow {x^2} - x + \frac{1}{4} - \frac{7}{4} = 0 \Leftrightarrow {\left( {x - \frac{1}{2}} \right)^2} = \frac{7}{4}\)

\( \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x - \frac{1}{2} = \frac{{\sqrt 7 }}{2}}\\{x - \frac{1}{2} = - \frac{{\sqrt 7 }}{2}}\end{array}} \right. \Leftrightarrow \left[ {\begin{array}{*{20}{c}}{x = \frac{{\sqrt 7 + 1}}{2}}\\{x = - \frac{{\sqrt 7 - 1}}{2}}\end{array}} \right.\).