\[0,5x^{2} - x - 0,5 =\]
\[= 0,5\left( x - 1 + \sqrt{2} \right)\left( x + 1 + \sqrt{2} \right).\]
\[0,5x^{2} - x - 0,5 = 0\ \ | \cdot 2\]
\[x^{2} - 2x - 1 = 0\]
\[D_{1} = 1 + 1 = 2\]
\[x_{1} = 1 + \sqrt{2};\]
\[x_{2} = 1 - \sqrt{2}.\]