Solve the quadratic inequality \(x^2 - 3x - 4 > 0\)

Step 1 ：First, we solve the corresponding equation \(x^2 - 3x - 4 = 0\)

Step 2 ：This can be factored into \((x - 4)(x + 1) = 0\)

Step 3 ：The solutions are \(x = 4\) and \(x = -1\)

Step 4 ：Now we consider the inequality \(x^2 - 3x - 4 > 0\)

Step 5 ：The parabola \(y = x^2 - 3x - 4\) opens upwards, and the roots of the equation are the x-coordinates of the vertex.

Step 6 ：We know that the y-values are positive when x is less than -1 or x is greater than 4.

Step 7 ：Therefore, the solution set for \(x^2 - 3x - 4 > 0\) is \(x < -1\) or \(x > 4\)