3^5/3x=3x

Solution for 3^5/3x=3x equation:

3^5/3x=3x

We move all terms to the left:

3^5/3x-(3x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-3x+3^5/3x=0

We multiply all the terms by the denominator


-3x*3x+3^5=0

We add all the numbers together, and all the variables

-3x*3x+243=0

Wy multiply elements

-9x^2+243=0

a = -9; b = 0; c = +243;
Δ = b2-4ac
Δ = 02-4·(-9)·243
Δ = 8748
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:

$\sqrt{\Delta}=\sqrt{8748}=\sqrt{2916*3}=\sqrt{2916}*\sqrt{3}=54\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-54\sqrt{3}}{2*-9}=\frac{0-54\sqrt{3}}{-18}
=-\frac{54\sqrt{3}}{-18}
=-\frac{3\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+54\sqrt{3}}{2*-9}=\frac{0+54\sqrt{3}}{-18}
=\frac{54\sqrt{3}}{-18}
=\frac{3\sqrt{3}}{-1}
$