sqrt(4-x^2)>30 inequation

Given the inequality:
$$\sqrt{4 - x^{2}} > 30$$
To solve this inequality, we must first solve the corresponding equation:
$$\sqrt{4 - x^{2}} = 30$$
Solve:
Given the equation
$$\sqrt{4 - x^{2}} = 30$$
$$\sqrt{4 - x^{2}} = 30$$
We raise the equation sides to 2-th degree
$$4 - x^{2} = 900$$
$$4 - x^{2} = 900$$
Transfer the right side of the equation left part with negative sign
$$- x^{2} - 896 = 0$$
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
$$a = -1$$
$$b = 0$$
$$c = -896$$
, then

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

(0)^2 - 4 * (-1) * (-896) = -3584

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
$$x_{1} = - 8 \sqrt{14} i$$
$$x_{2} = 8 \sqrt{14} i$$
$$x_{1} = - 8 \sqrt{14} i$$
$$x_{2} = 8 \sqrt{14} i$$
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

$$\sqrt{4 - 0^{2}} > 30$$

2 > 30

so the inequality has no solutions