Find the value of x when 2x^2 - x - 6 = 0

2x² - x - 6 = 0

This must first be factorised - I use the 'box method' when the reciprocal of x² is >1. This is difficult to explain via writing but it involves a little trial and error.

2x + 3 --> (+3x)

x - 2 --> (-4x)

Therefore 2x² - x - 6 = 0 can be factorised to give (2x+3)(x-2) = 0 - At this stage, you should multiply it out to check that you get the original equation. 

if 2x+3 = 0 --> 2x= -3 giving x = -3/2

if x-2 = 0  --> x = 2

Final check can be done by substituting each value of x into the original equation and ensuring the answer is 0.