9x/1=3-x/3*81x

Solution for 9x/1=3-x/3*81x equation:

9x/1=3-x/3*81x

We move all terms to the left:

9x/1-(3-x/3*81x)=0


Domain of the equation: 3*81x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x/1-(-x/3*81x+3)=0

We get rid of parentheses

9x/1+x/3*81x-3=0

We calculate fractions


17496x^2/1944x+x/1944x-3=0

We multiply all the terms by the denominator


17496x^2+x-3*1944x=0

Wy multiply elements

17496x^2+x-5832x=0

We add all the numbers together, and all the variables

17496x^2-5831x=0

a = 17496; b = -5831; c = 0;
Δ = b2-4ac
Δ = -58312-4·17496·0
Δ = 34000561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{34000561}=5831$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5831)-5831}{2*17496}=\frac{0}{34992}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5831)+5831}{2*17496}=\frac{11662}{34992}
=5831/17496
$