Hello , please guide me .
How can I transformed the equation $\displaystyle x^{5}-x^{4}-x^{3}-x^{2}-x-1 =0 $to $\displaystyle y^{5}+2y^{2}+47y+122 $ ?
I studied a lecture that the writer had written :<< by using $\displaystyle y=x^{2}-3x$ we can transformed $\displaystyle x^{5}-x^{4}-x^{3}-x^{2}-x-1 =0$ to $\displaystyle y^{5}+2y^{2}+47y+122 $ But how ? if in $\displaystyle y=x^2-3x $ we obtain $\displaystyle x$ by $\displaystyle y$ we will have : $\displaystyle x=3/2+\sqrt{y+9/4}$ and if we substitute $\displaystyle x=3/2+\sqrt{y+9/4}$ in $\displaystyle x^{5}-x^{4}-x^{3}-x^{2}-x-1 =0$ we don't have $y^5+2y^2+47y+122$ . please explain it.
Thank you very much