For what values of x is 2x^2 - 11x - 6 > 0 ?

The first step is to factorise the equation into two brackets. In this case we get (2x+1)(x-6)Now, for this to be greater than zero we need both brackets to be greater than zero, or both brackets to be less than zero. If one bracket was positive and the other negative, then the equation would be negative overall.So firstly, if they are both positive, 2x+1 > 0 tells us that x > -1/2. x - 6 > 0 tells us that x > 6. If we put these together then both inequalities have to be satisfied, so x has be be greater than 6. Now if they are both negative, 2x+1 < 0 tells us that x < -1/2. x-6 <0 tells us that x < 6. So overall x < -1/2 in order to satisfy both. So to conclude, we need x > 6 or x < -1/2 for the equation to be greater than zero.