a) \(0,5 - 0,6x = 0,7\)

\(0,6x = 0,5 - 0,7\)

\(0,6x =  - 0,2\)

\(x =  - 0,2:0,6\)

\(x =  - \frac{2}{{10}}:\frac{6}{{10}}\)

\(x =  - \frac{2}{{10}}.\frac{{10}}{6}\)

\(x =  - \frac{1}{3}\)

Vậy \(x =  - \frac{1}{3}\).

b) \(\frac{3}{4} - x =  - \frac{1}{5}\)

\(x = \frac{3}{4} - \left( { - \frac{1}{5}} \right)\)

\(x = \frac{3}{4} + \frac{1}{5}\)

\(x = \frac{{15}}{{20}} + \frac{4}{{20}}\)

\(x = \frac{{19}}{{20}}\)

Vậy \(x = \frac{{19}}{{20}}\).

c) \(\frac{3}{5}:\left( {\frac{1}{3} + \frac{2}{3}x} \right) = \frac{{ - 2}}{{25}}\)

\(\frac{1}{3} + \frac{2}{3}x = \frac{3}{5}:\left( {\frac{{ - 2}}{{25}}} \right)\)

\(\frac{1}{3} + \frac{2}{3}x = \frac{3}{5}.\frac{{25}}{{ - 2}}\)

\(\frac{1}{3} + \frac{2}{3}x = \frac{{ - 15}}{2}\)

\(\frac{2}{3}x = \frac{{ - 15}}{2} - \frac{1}{3}\)

\(\frac{2}{3}x = \frac{{ - 47}}{6}\)

\(x = \frac{{ - 47}}{6}:\frac{2}{3}\)

\(x = \frac{{ - 47}}{4}\)

Vậy \(x = \frac{{ - 47}}{4}\).

d) \(3.{\left( {x - \frac{1}{4}} \right)^2} = \frac{{27}}{4}\)

       \({\left( {x - \frac{1}{4}} \right)^2} = \frac{{27}}{4}:3 = \frac{9}{4}\)

       \({\left( {x - \frac{1}{4}} \right)^2} = {\left( {\frac{3}{2}} \right)^2} = {\left( { - \frac{3}{2}} \right)^2}\)

Trường hợp 1:

\(x - \frac{1}{4} = \frac{3}{2}\)

\(x = \frac{3}{2} + \frac{1}{4}\)

\(x = \frac{7}{4}\)

Vậy \[x \in \left\{ {\frac{7}{4}; - \frac{5}{4}} \right\}\].

Trường hợp 2:

\(x - \frac{1}{4} =  - \frac{3}{2}\)

\(x =  - \frac{3}{2} + \frac{1}{4}\)

\(x =  - \frac{5}{4}\)