9n^-144=(3n+12)(3n-12)

Solution for 9n^-144=(3n+12)(3n-12) equation:

9n^-144=(3n+12)(3n-12)

We move all terms to the left:

9n^-144-((3n+12)(3n-12))=0

We add all the numbers together, and all the variables

9n-((3n+12)(3n-12))-144=0

We use the square of the difference formula

9n^2+9n+144-144=0

We add all the numbers together, and all the variables

9n^2+9n=0

a = 9; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·9·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*9}=\frac{-18}{18}
=-1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*9}=\frac{0}{18}
=0
$