Solve the inequation x^2 - 4x - 12 > 0

First of all, we'll solve the qudratic equation:

x^2 -4x -12 = 0

After that, to find out the roots of the equation, we'll use the quadratic formula:

x1 = [-b + sqrt(b^2 - 4ac)]/2a, where a=1, b=-4, c =-12

x2 = [-b + sqrt(b^2 - 4ac)]/2a,

after calculation

x1=6, x2=-2

After that, following the rule which says that between the two roots, the values of function have the opposite sign of the "a" coefficient, and outside the roots, the values of the function have the same sign with the coefficient "a", we could find the conclusion that inequation is positive on the following intervals:

x belongs to the interval (-infinite, -2) U (6, + infinite).