0.64-25x^2<0 inequation

Given the inequality:
$$\frac{16}{25} - 25 x^{2} < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{16}{25} - 25 x^{2} = 0$$
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
$$a = -25$$
$$b = 0$$
$$c = \frac{16}{25}$$
, then

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

(0)^2 - 4 * (-25) * (16/25) = 64

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

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

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

or
$$x_{1} = - \frac{4}{25}$$
$$x_{2} = \frac{4}{25}$$
$$x_{1} = - \frac{4}{25}$$
$$x_{2} = \frac{4}{25}$$
$$x_{1} = - \frac{4}{25}$$
$$x_{2} = \frac{4}{25}$$
This roots
$$x_{1} = - \frac{4}{25}$$
$$x_{2} = \frac{4}{25}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{4}{25} + - \frac{1}{10}$$
=
$$- \frac{13}{50}$$
substitute to the expression
$$\frac{16}{25} - 25 x^{2} < 0$$
$$\frac{16}{25} - 25 \left(- \frac{13}{50}\right)^{2} < 0$$

-21     
---- < 0
 20     

one of the solutions of our inequality is:
$$x < - \frac{4}{25}$$

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

Other solutions will get with the changeover to the next point
etc.
The answer:
$$x < - \frac{4}{25}$$
$$x > \frac{4}{25}$$