3^2x-1=1/9

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

3^2x-1=1/9

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3^2x*9-10=0

Wy multiply elements

27x^2-10=0

a = 27; b = 0; c = -10;
Δ = b2-4ac
Δ = 02-4·27·(-10)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{30}}{2*27}=\frac{0-6\sqrt{30}}{54}
=-\frac{6\sqrt{30}}{54}
=-\frac{\sqrt{30}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{30}}{2*27}=\frac{0+6\sqrt{30}}{54}
=\frac{6\sqrt{30}}{54}
=\frac{\sqrt{30}}{9}
$