\(x^{2} - x - 1 = 0\)

Using the quadratic formula, 

\(x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}\)

a = 1, b = -1, c = -1.

\(x = \frac{-(-1) \pm \sqrt{(-1)^{2} - 4(1)(-1)}}{2(1)}\)

\(x = \frac{1 \pm \sqrt{1 + 4}}{2} = \frac{1 \pm \sqrt{5}}{2}\)

\(x = \frac{1 + 2.24}{2} ; x = \frac{1 - 2.24}{2}\)

\(x = \frac{3.24}{2}; x = \frac{-1.24}{2}\)

\(x = 1.62 ; x = -0.61 \)

\(x \approxeq 1.6; -0.6\)