8x^2-72x+144>0 inequation

Given the inequality:
$$8 x^{2} - 72 x + 144 > 0$$
To solve this inequality, we must first solve the corresponding equation:
$$8 x^{2} - 72 x + 144 = 0$$
Solve:
This equation is of the form
$$a\ x^2 + b\ x + c = 0$$
A quadratic equation can be solved using the discriminant
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 8$$
$$b = -72$$
$$c = 144$$
, then
$$D = b^2 - 4\ a\ c = $$
$$\left(-1\right) 8 \cdot 4 \cdot 144 + \left(-72\right)^{2} = 576$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = 6$$
Simplify
$$x_{2} = 3$$
Simplify
$$x_{1} = 6$$
$$x_{2} = 3$$
$$x_{1} = 6$$
$$x_{2} = 3$$
This roots
$$x_{2} = 3$$
$$x_{1} = 6$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{2}$$
For example, let's take the point
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 3$$
=
$$\frac{29}{10}$$
substitute to the expression
$$8 x^{2} - 72 x + 144 > 0$$
$$- \frac{29 \cdot 72}{10} + 8 \left(\frac{29}{10}\right)^{2} + 144 > 0$$

62    
-- > 0
25    

one of the solutions of our inequality is:
$$x < 3$$

 _____           _____          
      \         /
-------ο-------ο-------
       x_2      x_1

Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < 3$$
$$x > 6$$