\(3x^4-20x^3+35x^2+10x-48=0\)
\(\Leftrightarrow\left(x^2-2x-3\right)\left(3x^2-14x+16\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-3\right)\left(3x-8\right)\left(x-2\right)=0\)
\(\Rightarrow x=\left\{-1;3;\frac{8}{3};2\right\}\)
\(3x^4-20x^3+35x^2+10x-48=0\)
\(\Leftrightarrow3x^4-6x^3-9x^2-14x^3+28x^2+42x+16x^2-32x-48\)
\(\Leftrightarrow3x^2\left(x^2-2x-3\right)-14x\left(x^2-2x-3\right)+16\left(x^2-2x-3\right)=0\)
\(\Leftrightarrow\left(x^2-2x-3\right)\left(3x^2-14x+16\right)=0\)
\(\Leftrightarrow\left(x^2+x-3x-3\right)\left(3x^2-6x-8x+16\right)=0\)
\(\Leftrightarrow\left(x+1\right)\left(x-3\right)\left(x-2\right)\left(3x-8\right)=0\)
\(\Leftrightarrow S=\left\{-1;3;2;\frac{8}{3}\right\}\)
