Given quadratic equation is 2x^{2} – x – 6 = 0

⇒ 2x^{2} – 4x + 3x – 6 = 0

⇒ 2x (x – 2) + 3 (x – 2) = 0

⇒ (2x + 3) (x – 2) = 0

⇒ 2x + 3 = 0 or x –2 = 0

⇒ x = \(\frac{-3}2\) or x = 2.

Hence, the roots of the quadratic equation 2x^{2} – x – 6 = 0 are \(\frac{-3}2\) and 2.