6^2x-1=1/216

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

6^2x-1=1/216

We move all terms to the left:

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

We add all the numbers together, and all the variables

6^2x-1-(+1/216)=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}
$