x/3^2x=27

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

x/3^2x=27

We move all terms to the left:

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


Domain of the equation: 3^2x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


x-27*3^2x=0

Wy multiply elements

-81x^2+x=0

a = -81; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-81)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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