9n^2-4=464

Solution for 9n^2-4=464 equation:

9n^2-4=464

We move all terms to the left:

9n^2-4-(464)=0

We add all the numbers together, and all the variables

9n^2-468=0

a = 9; b = 0; c = -468;
Δ = b2-4ac
Δ = 02-4·9·(-468)
Δ = 16848
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:

$\sqrt{\Delta}=\sqrt{16848}=\sqrt{1296*13}=\sqrt{1296}*\sqrt{13}=36\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{13}}{2*9}=\frac{0-36\sqrt{13}}{18}
=-\frac{36\sqrt{13}}{18}
=-2\sqrt{13}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{13}}{2*9}=\frac{0+36\sqrt{13}}{18}
=\frac{36\sqrt{13}}{18}
=2\sqrt{13}
$