sqrt(x)*2-2*x-24>-4 inequation

Given the inequality:
$$\left(2 \sqrt{x} - 2 x\right) - 24 > -4$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(2 \sqrt{x} - 2 x\right) - 24 = -4$$
Solve:
Given the equation
$$\left(2 \sqrt{x} - 2 x\right) - 24 = -4$$
$$2 \sqrt{x} = 2 x + 20$$
We raise the equation sides to 2-th degree
$$4 x = \left(2 x + 20\right)^{2}$$
$$4 x = 4 x^{2} + 80 x + 400$$
Transfer the right side of the equation left part with negative sign
$$- 4 x^{2} - 76 x - 400 = 0$$
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
$$a = -4$$
$$b = -76$$
$$c = -400$$
, then

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

(-76)^2 - 4 * (-4) * (-400) = -624

Because D<0, then the equation
has no real roots,
but complex roots is exists.

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

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

or
$$x_{1} = - \frac{19}{2} - \frac{\sqrt{39} i}{2}$$
$$x_{2} = - \frac{19}{2} + \frac{\sqrt{39} i}{2}$$
$$x_{1} = - \frac{19}{2} - \frac{\sqrt{39} i}{2}$$
$$x_{2} = - \frac{19}{2} + \frac{\sqrt{39} i}{2}$$
Exclude the complex solutions:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example

x0 = 0

$$-24 + \left(2 \sqrt{0} - 0 \cdot 2\right) > -4$$

-24 > -4

so the inequality has no solutions