3^x*19683^x=9

Solution for 3^x*19683^x=9 equation:

3^x*19683^x=9

We move all terms to the left:

3^x*19683^x-(9)=0

Wy multiply elements

59049x^2-9=0

a = 59049; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·59049·(-9)
Δ = 2125764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2125764}=1458$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-1458}{2*59049}=\frac{-1458}{118098}
=-1/81
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+1458}{2*59049}=\frac{1458}{118098}
=1/81
$