9n^2+12n+9=81

Solution for 9n^2+12n+9=81 equation:

9n^2+12n+9=81

We move all terms to the left:

9n^2+12n+9-(81)=0

We add all the numbers together, and all the variables

9n^2+12n-72=0

a = 9; b = 12; c = -72;
Δ = b2-4ac
Δ = 122-4·9·(-72)
Δ = 2736
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:

$\sqrt{\Delta}=\sqrt{2736}=\sqrt{144*19}=\sqrt{144}*\sqrt{19}=12\sqrt{19}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12\sqrt{19}}{2*9}=\frac{-12-12\sqrt{19}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12\sqrt{19}}{2*9}=\frac{-12+12\sqrt{19}}{18}
$