arctg(2x^2-5x-1)+arctg(x^2-2x+5)≤0 inequation

Given the inequality:
$$\operatorname{atan}{\left(\left(x^{2} - 2 x\right) + 5 \right)} + \operatorname{atan}{\left(\left(2 x^{2} - 5 x\right) - 1 \right)} \leq 0$$
To solve this inequality, we must first solve the corresponding equation:
$$\operatorname{atan}{\left(\left(x^{2} - 2 x\right) + 5 \right)} + \operatorname{atan}{\left(\left(2 x^{2} - 5 x\right) - 1 \right)} = 0$$
Solve:
$$x_{1} = 1$$
$$x_{2} = \frac{4}{3}$$
$$x_{1} = 1$$
$$x_{2} = \frac{4}{3}$$
This roots
$$x_{1} = 1$$
$$x_{2} = \frac{4}{3}$$
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
$$x_{0} = x_{1} - \frac{1}{10}$$
=
$$- \frac{1}{10} + 1$$
=
$$\frac{9}{10}$$
substitute to the expression
$$\operatorname{atan}{\left(\left(x^{2} - 2 x\right) + 5 \right)} + \operatorname{atan}{\left(\left(2 x^{2} - 5 x\right) - 1 \right)} \leq 0$$
$$\operatorname{atan}{\left(\left(- \frac{5 \cdot 9}{10} + 2 \left(\frac{9}{10}\right)^{2}\right) - 1 \right)} + \operatorname{atan}{\left(\left(- \frac{2 \cdot 9}{10} + \left(\frac{9}{10}\right)^{2}\right) + 5 \right)} \leq 0$$

      /97\       /401\     
- atan|--| + atan|---| <= 0
      \25/       \100/     

but

      /97\       /401\     
- atan|--| + atan|---| >= 0
      \25/       \100/     

Then
$$x \leq 1$$
no execute
one of the solutions of our inequality is:
$$x \geq 1 \wedge x \leq \frac{4}{3}$$

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