\(\left(x+2\right)\left(x^2-2x+4\right)-x\left(x^2-2\right)=15\)
\(\Leftrightarrow x^3+8-x^3+2x=15\)
\(\Leftrightarrow2x+8=15\)
\(\Leftrightarrow2x=15-8=7\)
\(\Leftrightarrow x=\frac{7}{2}\)
\(\left(x+2\right)\left(x^2-2x+4\right)-x.\left(x^2-2\right)=15\)