[tex]\dfrac{1-4x}{x}=\dfrac{7-20x}{1+4x}+\dfrac{3}{x+4x^{2}}\\\\\\
\dfrac{1-4x}{x}=\dfrac{7-20x}{1+4x}+\dfrac{3}{x(1+4x)}\\\\\\
\dfrac{(1-4x)(1+4x)}{x(1+4x)}=\dfrac{(7-20x)x}{(1+4x)x}+\dfrac{3}{x(1+4x)}\\\\
(1-4x)(1+4x)=(7-20x)x+3\\\\
1-16x^{2}=7x-20x^{2}+3\\\\
4x^{2}-7x-2=0[/tex]
[tex]\Delta=b^{2}-4\cdot a\cdot c\\
\Delta=(-7)^{2}-4\cdot4\cdot(-2)\\ \Delta=49+32\\ \Delta=81\\\\ x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{7\pm\sqrt{81}}{2\cdot4}\\\\x=\dfrac{7\pm9}{8}[/tex]
[tex]\Longrightarrow x_{1}=\dfrac{7+9}{8}=\dfrac{16}{8}=2\\\\ \Longrightarrow x_{2}=\dfrac{7-9}{8}=\dfrac{-2}{8}=-\dfrac{1}{4}[/tex]
[tex]S=\{-\dfrac{1}{4},\;2\}[/tex]
