9n*3n=8316

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Solution for 9n*3n=8316 equation:



9n*3n=8316
We move all terms to the left:
9n*3n-(8316)=0
Wy multiply elements
27n^2-8316=0
a = 27; b = 0; c = -8316;
Δ = b2-4ac
Δ = 02-4·27·(-8316)
Δ = 898128
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:
$\sqrt{\Delta}=\sqrt{898128}=\sqrt{11664*77}=\sqrt{11664}*\sqrt{77}=108\sqrt{77}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-108\sqrt{77}}{2*27}=\frac{0-108\sqrt{77}}{54} =-\frac{108\sqrt{77}}{54} =-2\sqrt{77} $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+108\sqrt{77}}{2*27}=\frac{0+108\sqrt{77}}{54} =\frac{108\sqrt{77}}{54} =2\sqrt{77} $

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