4/27=3^2x

Solution for 4/27=3^2x equation:

4/27=3^2x

We move all terms to the left:

4/27-(3^2x)=0

We multiply all the terms by the denominator


-3^2x*27+4=0

Wy multiply elements

-81x^2+4=0

a = -81; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-81)·4
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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