3^x*9^x=9^3

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

3^x*9^x=9^3

We move all terms to the left:

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

We add all the numbers together, and all the variables

3^x*9^x-729=0

Wy multiply elements

27x^2-729=0

a = 27; b = 0; c = -729;
Δ = b2-4ac
Δ = 02-4·27·(-729)
Δ = 78732
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:

$\sqrt{\Delta}=\sqrt{78732}=\sqrt{26244*3}=\sqrt{26244}*\sqrt{3}=162\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-162\sqrt{3}}{2*27}=\frac{0-162\sqrt{3}}{54}
=-\frac{162\sqrt{3}}{54}
=-3\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+162\sqrt{3}}{2*27}=\frac{0+162\sqrt{3}}{54}
=\frac{162\sqrt{3}}{54}
=3\sqrt{3}
$