(x-11)(x-2.3)=<0 inequation

Given the inequality:
$$\left(x - 11\right) \left(x - \frac{23}{10}\right) \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\left(x - 11\right) \left(x - \frac{23}{10}\right) = 0$$
Solve:
Expand the expression in the equation
$$\left(x - 11\right) \left(x - \frac{23}{10}\right) = 0$$
We get the quadratic equation
$$x^{2} - \frac{133 x}{10} + \frac{253}{10} = 0$$
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
$$a = 1$$
$$b = - \frac{133}{10}$$
$$c = \frac{253}{10}$$
, then

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

(-133/10)^2 - 4 * (1) * (253/10) = 7569/100

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

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

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

or
$$x_{1} = 11$$
$$x_{2} = \frac{23}{10}$$
$$x_{1} = 11$$
$$x_{2} = \frac{23}{10}$$
$$x_{1} = 11$$
$$x_{2} = \frac{23}{10}$$
This roots
$$x_{2} = \frac{23}{10}$$
$$x_{1} = 11$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} \leq x_{2}$$
For example, let's take the point
$$x_{0} = x_{2} - \frac{1}{10}$$
=
$$- \frac{1}{10} + \frac{23}{10}$$
=
$$\frac{11}{5}$$
substitute to the expression
$$\left(x - 11\right) \left(x - \frac{23}{10}\right) \leq 0$$
$$\left(-11 + \frac{11}{5}\right) \left(- \frac{23}{10} + \frac{11}{5}\right) \leq 0$$

22     
-- <= 0
25     

but

22     
-- >= 0
25     

Then
$$x \leq \frac{23}{10}$$
no execute
one of the solutions of our inequality is:
$$x \geq \frac{23}{10} \wedge x \leq 11$$

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       x2      x1