216^2m=1/36

Solution for 216^2m=1/36 equation:

216^2m=1/36

We move all terms to the left:

216^2m-(1/36)=0

We add all the numbers together, and all the variables

216^2m-(+1/36)=0

We get rid of parentheses

216^2m-1/36=0

We multiply all the terms by the denominator


216^2m*36-1=0

Wy multiply elements

7776m^2-1=0

a = 7776; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·7776·(-1)
Δ = 31104
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{31104}=\sqrt{5184*6}=\sqrt{5184}*\sqrt{6}=72\sqrt{6}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{6}}{2*7776}=\frac{0-72\sqrt{6}}{15552}
=-\frac{72\sqrt{6}}{15552}
=-\frac{\sqrt{6}}{216}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{6}}{2*7776}=\frac{0+72\sqrt{6}}{15552}
=\frac{72\sqrt{6}}{15552}
=\frac{\sqrt{6}}{216}
$