--2(1-x)*(2*x+5)>=0 inequation

Given the inequality:
$$2 \left(1 - x\right) \left(2 x + 5\right) \geq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$2 \left(1 - x\right) \left(2 x + 5\right) = 0$$
Solve:
Expand the expression in the equation
$$2 \left(1 - x\right) \left(2 x + 5\right) = 0$$
We get the quadratic equation
$$- 4 x^{2} - 6 x + 10 = 0$$
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
$$a = -4$$
$$b = -6$$
$$c = 10$$
, then

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

(-6)^2 - 4 * (-4) * (10) = 196

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

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

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

or
$$x_{1} = - \frac{5}{2}$$
$$x_{2} = 1$$
$$x_{1} = - \frac{5}{2}$$
$$x_{2} = 1$$
$$x_{1} = - \frac{5}{2}$$
$$x_{2} = 1$$
This roots
$$x_{1} = - \frac{5}{2}$$
$$x_{2} = 1$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{1}$$
For example, let's take the point
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{5}{2} + - \frac{1}{10}$$
=
$$- \frac{13}{5}$$
substitute to the expression
$$2 \left(1 - x\right) \left(2 x + 5\right) \geq 0$$
$$2 \left(1 - - \frac{13}{5}\right) \left(\frac{\left(-13\right) 2}{5} + 5\right) \geq 0$$

-36      
---- >= 0
 25      

but

-36     
---- < 0
 25     

Then
$$x \leq - \frac{5}{2}$$
no execute
one of the solutions of our inequality is:
$$x \geq - \frac{5}{2} \wedge x \leq 1$$

         _____  
        /     \  
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       x1      x2