Given the inequality:
$$\frac{\log{\left(1 \right)}}{5} \left(x^{2} - \frac{4}{5}\right) > 1$$
To solve this inequality, we must first solve the corresponding equation:
$$\frac{\log{\left(1 \right)}}{5} \left(x^{2} - \frac{4}{5}\right) = 1$$
Solve:
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
$$\frac{\log{\left(1 \right)}}{5} \left(- \frac{4}{5} + 0^{2}\right) > 1$$
0 > 1
so the inequality has no solutions