Show that the roots of the equation \( x^{2}+2(3 a+5) x+2\left(9 a^{2}+25\right)=0 \) are comple...

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Show that the roots of the equation \( x^{2}+2(3 a+5) x+2\left(9 a^{2}+25\right)=0 \) are complex unless
\[
a=\frac{5}{3} .
\]
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