The roots of polynomial $ p(a) $ are:
$$ \begin{aligned}a_1 &= 6.0662\\[1 em]a_2 &= -2.6376 \end{aligned} $$The solutions of $ 7a^2-24a-112 = 0 $ are: $ a = \dfrac{ 12 }{ 7 }-\dfrac{ 4 \sqrt{ 58}}{ 7 } ~ \text{and} ~ a = \dfrac{ 12 }{ 7 }+\dfrac{ 4 \sqrt{ 58}}{ 7 }$.
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