$\begin{array} { l }\frac{ 5 }{ a }+\frac{ 7 }{ 2 }=-\frac{ 7 }{ 5 }+\frac{ 3 }{ 2a },& a≠0\end{array}$
Move the expression to the left-hand side and change its sign$\frac{ 5 }{ a }+\frac{ 7 }{ 2 }-\frac{ 3 }{ 2a }=-\frac{ 7 }{ 5 }$
Move the constant to the right-hand side and change its sign$\frac{ 5 }{ a }-\frac{ 3 }{ 2a }=-\frac{ 7 }{ 5 }-\frac{ 7 }{ 2 }$
Write all numerators above the least common denominator $2a$$\frac{ 7 }{ 2a }=-\frac{ 7 }{ 5 }-\frac{ 7 }{ 2 }$
Calculate the difference$\frac{ 7 }{ 2a }=-\frac{ 49 }{ 10 }$
Simplify the equation using cross-multiplication$70=-98a$
Swap the sides of the equation$-98a=70$
Divide both sides of the equation by $-98$$\begin{array} { l }a=-\frac{ 5 }{ 7 },& a≠0\end{array}$
Check if the solution is in the defined range$\begin{align*}&a=-\frac{ 5 }{ 7 } \\&a=-0.\overset{ \cdot }{ 7 } 1428\overset{ \cdot }{ 5 } \end{align*}$