4-9x²<0 inequation

Given the inequality:
$$4 - 9 x^{2} < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$4 - 9 x^{2} = 0$$
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 - it is the discriminant.
Because
$$a = -9$$
$$b = 0$$
$$c = 4$$
, then

D = b^2 - 4 * a * c = 

(0)^2 - 4 * (-9) * (4) = 144

Because D > 0, then the equation has two roots.

x1 = (-b + sqrt(D)) / (2*a)

x2 = (-b - sqrt(D)) / (2*a)

or
$$x_{1} = - \frac{2}{3}$$
$$x_{2} = \frac{2}{3}$$
$$x_{1} = - \frac{2}{3}$$
$$x_{2} = \frac{2}{3}$$
$$x_{1} = - \frac{2}{3}$$
$$x_{2} = \frac{2}{3}$$
This roots
$$x_{1} = - \frac{2}{3}$$
$$x_{2} = \frac{2}{3}$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{2}{3} + - \frac{1}{10}$$
=
$$- \frac{23}{30}$$
substitute to the expression
$$4 - 9 x^{2} < 0$$
$$4 - 9 \left(- \frac{23}{30}\right)^{2} < 0$$

-129     
----- < 0
 100     

one of the solutions of our inequality is:
$$x < - \frac{2}{3}$$

 _____           _____          
      \         /
-------ο-------ο-------
       x1      x2

Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < - \frac{2}{3}$$
$$x > \frac{2}{3}$$