3/n^2=729

Solution for 3/n^2=729 equation:

3/n^2=729

We move all terms to the left:

3/n^2-(729)=0


Domain of the equation: n^2!=0

n^2!=0/

n^2!=√0

n!=0

n∈R


We multiply all the terms by the denominator


-729*n^2+3=0

We add all the numbers together, and all the variables

-729n^2+3=0

a = -729; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-729)·3
Δ = 8748
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:

$\sqrt{\Delta}=\sqrt{8748}=\sqrt{2916*3}=\sqrt{2916}*\sqrt{3}=54\sqrt{3}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54\sqrt{3}}{2*-729}=\frac{0-54\sqrt{3}}{-1458}
=-\frac{54\sqrt{3}}{-1458}
=-\frac{\sqrt{3}}{-27}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54\sqrt{3}}{2*-729}=\frac{0+54\sqrt{3}}{-1458}
=\frac{54\sqrt{3}}{-1458}
=\frac{\sqrt{3}}{-27}
$