3x(1/9^2x)=243

Solution for 3x(1/9^2x)=243 equation:

3x(1/9^2x)=243

We move all terms to the left:

3x(1/9^2x)-(243)=0


Domain of the equation: 9^2x)!=0

x!=0/1

x!=0

x∈R


We multiply parentheses

3x^2-243=0

a = 3; b = 0; c = -243;
Δ = b2-4ac
Δ = 02-4·3·(-243)
Δ = 2916
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2916}=54$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54}{2*3}=\frac{-54}{6}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54}{2*3}=\frac{54}{6}
=9
$