1/216=6^2x-1

Solution for 1/216=6^2x-1 equation:

1/216=6^2x-1

We move all terms to the left:

1/216-(6^2x-1)=0

We get rid of parentheses

-6^2x+1+1/216=0

We multiply all the terms by the denominator


-6^2x*216+1+1*216=0

We add all the numbers together, and all the variables

-6^2x*216+217=0

Wy multiply elements

-1296x^2+217=0

a = -1296; b = 0; c = +217;
Δ = b2-4ac
Δ = 02-4·(-1296)·217
Δ = 1124928
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:

$\sqrt{\Delta}=\sqrt{1124928}=\sqrt{5184*217}=\sqrt{5184}*\sqrt{217}=72\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-72\sqrt{217}}{2*-1296}=\frac{0-72\sqrt{217}}{-2592}
=-\frac{72\sqrt{217}}{-2592}
=-\frac{\sqrt{217}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+72\sqrt{217}}{2*-1296}=\frac{0+72\sqrt{217}}{-2592}
=\frac{72\sqrt{217}}{-2592}
=\frac{\sqrt{217}}{-36}
$