6^(2x)=1/36

Solution for 6^(2x)=1/36 equation:

6^(2x)=1/36

We move all terms to the left:

6^(2x)-(1/36)=0

We add all the numbers together, and all the variables

6^2x-(+1/36)=0

We get rid of parentheses

6^2x-1/36=0

We multiply all the terms by the denominator


6^2x*36-1=0

Wy multiply elements

216x^2-1=0

a = 216; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·216·(-1)
Δ = 864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{6}}{2*216}=\frac{0-12\sqrt{6}}{432}
=-\frac{12\sqrt{6}}{432}
=-\frac{\sqrt{6}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{6}}{2*216}=\frac{0+12\sqrt{6}}{432}
=\frac{12\sqrt{6}}{432}
=\frac{\sqrt{6}}{36}
$