Three, (12 points) Let the equation about $x$ be $x^{2}+\left(\frac{a}{x}\right)^{2}-7 x$ $-\frac{7 a}{x}+2 a+12=0$ and suppose it has equal roots. Find the value of $a$.

 untranslated portion: 

设关于 $x$ 的方程 $x^{2}+\left(\frac{a}{x}\right)^{2}-7 x$ $-\frac{7 a}{x}+2 a+12=0$ 有相等鳫根. 求 $a$ 的值.

translated portion:

Let the equation about $x$ be $x^{2}+\left(\frac{a}{x}\right)^{2}-7 x$ $-\frac{7 a}{x}+2 a+12=0$ and suppose it has equal roots. Find the value of $a$.