32n*27n=315

Solution for 32n*27n=315 equation:

32n*27n=315

We move all terms to the left:

32n*27n-(315)=0

Wy multiply elements

864n^2-315=0

a = 864; b = 0; c = -315;
Δ = b2-4ac
Δ = 02-4·864·(-315)
Δ = 1088640
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:

$\sqrt{\Delta}=\sqrt{1088640}=\sqrt{5184*210}=\sqrt{5184}*\sqrt{210}=72\sqrt{210}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{210}}{2*864}=\frac{0-72\sqrt{210}}{1728}
=-\frac{72\sqrt{210}}{1728}
=-\frac{\sqrt{210}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{210}}{2*864}=\frac{0+72\sqrt{210}}{1728}
=\frac{72\sqrt{210}}{1728}
=\frac{\sqrt{210}}{24}
$