$$\begin{gathered} a, 7x²+2x=0 \\ <=>x.\left(7x+2\right)=0 \\ <=>x=0 hoặc 7x+2=0 \\ <=>x=0 hoặc 7x=-2 \\ <=>x=0 hoặc x=-\frac{2}{7} \\ Vậy S=\left\{-\frac{2}{7};0\right\} \\ b, 4x² - 4x = -1 \\ <=>4x^2-4x+1=0 \\ <=>{\left(2x-1\right)}^2=0 \\ <=>2x-1=0 \\ <=>2x=1 \\ <=>x=\frac{1}{2} \\ Vậy x=\frac{1}{2} \\ c, x(x-2019) - x + 2019 = 0 \\ <=>x.\left(x-2019\right)-\left(x-2019\right)=0 \\ <=>\left(x-2019\right)\left(x-1\right)=0 \\ <=>x-2019=0 hoặc x-1=0 \\ <=>x=2019 hoặc x=1 \\ Vậy S=\left\{1;2019\right\} \\ d, (3x-4)²-(x + 2) ² = 0 \\ <=>\left(3x-4-x-2\right)\left(3x-4+x+2\right)=0 \\ <=>\left(2x-6\right)\left(4x-2\right)=0 \\ <=>2x-6=0 hoặc 4x-2=0 \\ <=>2x=6 hoặc 4x=2 \\ <=>x=3 hoặc x=\frac{1}{2} \\ Vậy S=\left\{3;\frac{1}{2}\right\} \end{gathered}$$.

\[\begin{array}{l}
a,{\rm{ }}7{x^2} + 2x = 0{\rm{ }}\\
\Leftrightarrow x\left( {7x + 2} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
7x + 2 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 0\\
x = \frac{{ - 2}}{7}
\end{array} \right.\\
Vay:S = \{ 0;\frac{{ - 2}}{7}\} \\
b,{\rm{ }}4{x^2} - {\rm{ }}4x{\rm{ }} = {\rm{ }} - 1\\
\Leftrightarrow 4{x^2} - 4x + 1 = 0\\
\Leftrightarrow {\left( {2x - 1} \right)^2} = 0\\
\Leftrightarrow 2x - 1 = 0\\
\Leftrightarrow x = \frac{1}{2}\\
Vay:x = \frac{1}{2}\\
{\rm{ }}c,{\rm{ }}x\left( {x - 2019} \right){\rm{ }} - {\rm{ }}x{\rm{ }} + {\rm{ }}2019{\rm{ }} = {\rm{ }}0{\rm{ }}\\
\Leftrightarrow x\left( {x - 2019} \right) - \left( {x - 2019} \right) = 0\\
\Leftrightarrow \left( {x - 2019} \right)\left( {x - 1} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 2019 = 0\\
x - 1 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 2019\\
x = 1
\end{array} \right.\\
vay:S = \{ 1;2019\} \\
d,{\rm{ }}{\left( {3x - 4} \right)^2} - {\left( {x{\rm{ }} + {\rm{ }}2} \right)^2}{\rm{ }} = {\rm{ }}0\\
\Leftrightarrow \left( {3x - 4 - x - 2} \right)\left( {3x - 4 + x + 2} \right) = 0\\
\Leftrightarrow \left( {2x - 6} \right)\left( {4x - 2} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
2x - 6 = 0\\
4x - 2 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 3\\
x = \frac{1}{2}
\end{array} \right.\\
vay:S = \{ 3;\frac{1}{2}\}
\end{array}\]