9^2x-8=1/9

Solution for 9^2x-8=1/9 equation:

9^2x-8=1/9

We move all terms to the left:

9^2x-8-(1/9)=0

We add all the numbers together, and all the variables

9^2x-8-(+1/9)=0

We get rid of parentheses

9^2x-8-1/9=0

We multiply all the terms by the denominator


9^2x*9-1-8*9=0

We add all the numbers together, and all the variables

9^2x*9-73=0

Wy multiply elements

81x^2-73=0

a = 81; b = 0; c = -73;
Δ = b2-4ac
Δ = 02-4·81·(-73)
Δ = 23652
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:

$\sqrt{\Delta}=\sqrt{23652}=\sqrt{324*73}=\sqrt{324}*\sqrt{73}=18\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{73}}{2*81}=\frac{0-18\sqrt{73}}{162}
=-\frac{18\sqrt{73}}{162}
=-\frac{\sqrt{73}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{73}}{2*81}=\frac{0+18\sqrt{73}}{162}
=\frac{18\sqrt{73}}{162}
=\frac{\sqrt{73}}{9}
$