81*3^2x/3^3=1

Solution for 81*3^2x/3^3=1 equation:

81*3^2x/3^3=1

We move all terms to the left:

81*3^2x/3^3-(1)=0

We multiply all the terms by the denominator


81*3^2x-1*3^3=0

We add all the numbers together, and all the variables

81*3^2x-27=0

Wy multiply elements

243x^2-27=0

a = 243; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·243·(-27)
Δ = 26244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26244}=162$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-162}{2*243}=\frac{-162}{486}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+162}{2*243}=\frac{162}{486}
=1/3
$