3^2x-9=1/27

Solution for 3^2x-9=1/27 equation:

3^2x-9=1/27

We move all terms to the left:

3^2x-9-(1/27)=0

We add all the numbers together, and all the variables

3^2x-9-(+1/27)=0

We get rid of parentheses

3^2x-9-1/27=0

We multiply all the terms by the denominator


3^2x*27-1-9*27=0

We add all the numbers together, and all the variables

3^2x*27-244=0

Wy multiply elements

81x^2-244=0

a = 81; b = 0; c = -244;
Δ = b2-4ac
Δ = 02-4·81·(-244)
Δ = 79056
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:

$\sqrt{\Delta}=\sqrt{79056}=\sqrt{1296*61}=\sqrt{1296}*\sqrt{61}=36\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36\sqrt{61}}{2*81}=\frac{0-36\sqrt{61}}{162}
=-\frac{36\sqrt{61}}{162}
=-\frac{2\sqrt{61}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36\sqrt{61}}{2*81}=\frac{0+36\sqrt{61}}{162}
=\frac{36\sqrt{61}}{162}
=\frac{2\sqrt{61}}{9}
$