\(\left(2x-5\right)^3-\left(x-2\right)^3=\left(x-3\right)^3\)
\(\Leftrightarrow\left(2x-5-x+2\right)\left(4x^2-20x+25+2x^2-9x+10+x^2-4x+4\right)=\left(x-3\right)^3\)
\(\Leftrightarrow\left(x-3\right)\left(7x^2-33x+39\right)-\left(x-3\right)^3=0\)
\(\Leftrightarrow\left(x-3\right)\left(7x^2-33x+39-x^2+6x-9\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(6x^2-27x+30\right)=0\)
\(\Leftrightarrow\left(x-3\right)3\left(2x^2-9x+10\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(2x^2-4x-5x+10\right)=0\)
\(\Leftrightarrow\left(x-3\right)[2x\left(x-2\right)-5\left(x-2\right)]=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(2x-5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-3=0\\x-2=0\\2x-5=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=3\\x=2\\x=\dfrac{5}{2}\end{matrix}\right.\)
\(S=\left\{2;\dfrac{5}{2};3\right\}\)
