Please say me where I am wrong.... or show me how to continue to solve this equation...
Thanks

is the comma supposed to be a dot in $\displaystyle 2 lg^3 x - 1,5x$

isn't it the same? you can write it like that: $\displaystyle $$\left( {2{{\lg }^3}x - {3 \over 2}x} \right) \cdot \lg x = {1 \over 2}$$$

if I remember correctly, the log symbology lg indicates a base 2 logarithm ... ?

... your work shows you are assuming it's a base 10 logarithm.

Getting back to the original equation, because you have the unknown, x, as base and in the exponent, there is not going to be any "algebraic" method. You might, with a lot of algebraic manipulation, get this into a form in which you could apply "Lambert's W function" (defined as the inverse function to $\displaystyle f(x)= xe^x$) but I don't see any simple way to do that.