((1/2)*x-2)^2<0 inequation

Given the inequality:
$$\left(\frac{x}{2} - 2\right)^{2} < 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(\frac{x}{2} - 2\right)^{2} = 0$$
Solve:
Expand the expression in the equation
$$\left(\frac{x}{2} - 2\right)^{2} = 0$$
We get the quadratic equation
$$\frac{x^{2}}{4} - 2 x + 4 = 0$$
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
$$a = \frac{1}{4}$$
$$b = -2$$
$$c = 4$$
, then

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

(-2)^2 - 4 * (1/4) * (4) = 0

Because D = 0, then the equation has one root.

x = -b/2a = --2/2/(1/4)

$$x_{1} = 4$$
$$x_{1} = 4$$
$$x_{1} = 4$$
This roots
$$x_{1} = 4$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 4$$
=
$$\frac{39}{10}$$
substitute to the expression
$$\left(\frac{x}{2} - 2\right)^{2} < 0$$
$$\left(-2 + \frac{39}{2 \cdot 10}\right)^{2} < 0$$

1/400 < 0

but

1/400 > 0

Then
$$x < 4$$
no execute
the solution of our inequality is:
$$x > 4$$

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