9n^2=864

Solution for 9n^2=864 equation:

9n^2=864

We move all terms to the left:

9n^2-(864)=0

a = 9; b = 0; c = -864;
Δ = b2-4ac
Δ = 02-4·9·(-864)
Δ = 31104
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:

$\sqrt{\Delta}=\sqrt{31104}=\sqrt{5184*6}=\sqrt{5184}*\sqrt{6}=72\sqrt{6}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{6}}{2*9}=\frac{0-72\sqrt{6}}{18}
=-\frac{72\sqrt{6}}{18}
=-4\sqrt{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{6}}{2*9}=\frac{0+72\sqrt{6}}{18}
=\frac{72\sqrt{6}}{18}
=4\sqrt{6}
$