-3(8n+7)2n=-99

Solution for -3(8n+7)2n=-99 equation:

-3(8n+7)2n=-99

We move all terms to the left:

-3(8n+7)2n-(-99)=0

We add all the numbers together, and all the variables

-3(8n+7)2n+99=0

We multiply parentheses

-48n^2-42n+99=0

a = -48; b = -42; c = +99;
Δ = b2-4ac
Δ = -422-4·(-48)·99
Δ = 20772
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20772}=\sqrt{36*577}=\sqrt{36}*\sqrt{577}=6\sqrt{577}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{577}}{2*-48}=\frac{42-6\sqrt{577}}{-96}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{577}}{2*-48}=\frac{42+6\sqrt{577}}{-96}
$