27*81^x=3^x2*27^x2

Solution for 27*81^x=3^x2*27^x2 equation:

27*81^x=3^x2*27^x2

We move all terms to the left:

27*81^x-(3^x2*27^x2)=0

Wy multiply elements

2187x-(3^x2*27^x2)=0

We get rid of parentheses

2187x-3^x2*27^x2=0

Wy multiply elements

-81x^2+2187x=0

a = -81; b = 2187; c = 0;
Δ = b2-4ac
Δ = 21872-4·(-81)·0
Δ = 4782969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4782969}=2187$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2187)-2187}{2*-81}=\frac{-4374}{-162}
=+27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2187)+2187}{2*-81}=\frac{0}{-162}
=0
$