9^x*81=9^15/x

Solution for 9^x*81=9^15/x equation:

9^x*81=9^15/x

We move all terms to the left:

9^x*81-(9^15/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


Wy multiply elements

729x-(9^15/x)=0

We get rid of parentheses

729x-9^15/x=0

We multiply all the terms by the denominator


729x*x-9^15=0

We add all the numbers together, and all the variables

729x*x-205891132094649=0

Wy multiply elements

729x^2-205891132094649=0

a = 729; b = 0; c = -205891132094649;
Δ = b2-4ac
Δ = 02-4·729·(-205891132094649)
Δ = 600378541187996484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{600378541187996484}=774840978$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-774840978}{2*729}=\frac{-774840978}{1458}
=-531441
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+774840978}{2*729}=\frac{774840978}{1458}
=531441
$