9^4+x=27^8/x

Solution for 9^4+x=27^8/x equation:

9^4+x=27^8/x

We move all terms to the left:

9^4+x-(27^8/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(27^8/x)+6561=0

We get rid of parentheses

x-27^8/x+6561=0

We multiply all the terms by the denominator


x*x+6561*x-27^8=0

We add all the numbers together, and all the variables

6561x+x*x-282429536481=0

Wy multiply elements

x^2+6561x-282429536481=0

a = 1; b = 6561; c = -282429536481;
Δ = b2-4ac
Δ = 65612-4·1·(-282429536481)
Δ = 1129761192645
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:

$\sqrt{\Delta}=\sqrt{1129761192645}=\sqrt{43046721*26245}=\sqrt{43046721}*\sqrt{26245}=6561\sqrt{26245}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6561)-6561\sqrt{26245}}{2*1}=\frac{-6561-6561\sqrt{26245}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6561)+6561\sqrt{26245}}{2*1}=\frac{-6561+6561\sqrt{26245}}{2}
$