9n^2-9=639

Solution for 9n^2-9=639 equation:

9n^2-9=639

We move all terms to the left:

9n^2-9-(639)=0

We add all the numbers together, and all the variables

9n^2-648=0

a = 9; b = 0; c = -648;
Δ = b2-4ac
Δ = 02-4·9·(-648)
Δ = 23328
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:

$\sqrt{\Delta}=\sqrt{23328}=\sqrt{11664*2}=\sqrt{11664}*\sqrt{2}=108\sqrt{2}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-108\sqrt{2}}{2*9}=\frac{0-108\sqrt{2}}{18}
=-\frac{108\sqrt{2}}{18}
=-6\sqrt{2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+108\sqrt{2}}{2*9}=\frac{0+108\sqrt{2}}{18}
=\frac{108\sqrt{2}}{18}
=6\sqrt{2}
$