Find values of x which satisfy the inequality: x^2-4x-2<10

We first apply a simple addition to make the inequality 0 on one side. We subtract 10, giving x^2-4x-12<0. Now we factorise the equation in x, intuitively or using the quadratic formula: x=(-b+sqrt(b^2-4ac))/2a or X==(-b-sqrt(b^2-4ac))/2a to give 2 values for x. In this case we can use intuition to get (X-6)(X+2)<0. We draw a graph of the function and deduce which values of X satisfy the inequality. Here, if -2 < x < 6 the inequality is satisfied.