Find the roots of the following equation:
$x - \frac{1}{x} = 3, x \neq 0$

(N/A) Given equation: $x - \frac{1}{x} = 3$
Multiply throughout by $x$ to get: $x^{2} - 1 = 3x$
Rearrange into standard quadratic form: $x^{2} - 3x - 1 = 0$
Comparing this with $ax^{2} + bx + c = 0$,we get $a = 1, b = -3, c = -1$.
Using the quadratic formula $x = \frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$:
$x = \frac{-(-3) \pm \sqrt{(-3)^{2} - 4(1)(-1)}}{2(1)}$
$x = \frac{3 \pm \sqrt{9 + 4}}{2}$
$x = \frac{3 \pm \sqrt{13}}{2}$
Thus,the roots are $x = \frac{3 + \sqrt{13}}{2}$ and $x = \frac{3 - \sqrt{13}}{2}$.