-9(6+n)2n=-10

Solution for -9(6+n)2n=-10 equation:

-9(6+n)2n=-10

We move all terms to the left:

-9(6+n)2n-(-10)=0

We add all the numbers together, and all the variables

-9(n+6)2n-(-10)=0

We add all the numbers together, and all the variables

-9(n+6)2n+10=0

We multiply parentheses

-18n^2-108n+10=0

a = -18; b = -108; c = +10;
Δ = b2-4ac
Δ = -1082-4·(-18)·10
Δ = 12384
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:

$\sqrt{\Delta}=\sqrt{12384}=\sqrt{144*86}=\sqrt{144}*\sqrt{86}=12\sqrt{86}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-12\sqrt{86}}{2*-18}=\frac{108-12\sqrt{86}}{-36}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+12\sqrt{86}}{2*-18}=\frac{108+12\sqrt{86}}{-36}
$