(sqrt14-4)*x<0 inequation

Given the inequality:
$$x \left(-4 + \sqrt{14}\right) < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$x \left(-4 + \sqrt{14}\right) = 0$$
Solve:
Given the linear equation:

(sqrt(14)-4)*x = 0

Expand brackets in the left part

sqrt+14-4)*x = 0

Move free summands (without x)
from left part to right part, we given:
$$x \left(-4 + \sqrt{14}\right) + 4 = 4$$
Divide both parts of the equation by (4 + x*(-4 + sqrt(14)))/x

x = 4 / ((4 + x*(-4 + sqrt(14)))/x)

$$x_{1} = 0$$
$$x_{1} = 0$$
This roots
$$x_{1} = 0$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10}$$
=
$$- \frac{1}{10}$$
substitute to the expression
$$x \left(-4 + \sqrt{14}\right) < 0$$
$$\frac{\left(-1\right) \left(-4 + \sqrt{14}\right)}{10} < 0$$

      ____    
2   \/ 14     
- - ------ < 0
5     10      
    

but

      ____    
2   \/ 14     
- - ------ > 0
5     10      
    

Then
$$x < 0$$
no execute
the solution of our inequality is:
$$x > 0$$

         _____  
        /
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       x1