27x=9(2x)-1/3x

Solution for 27x=9(2x)-1/3x equation:

27x=9(2x)-1/3x

We move all terms to the left:

27x-(9(2x)-1/3x)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

27x-(+92x-1/3x)=0

We get rid of parentheses

27x-92x+1/3x=0

We multiply all the terms by the denominator


27x*3x-92x*3x+1=0

Wy multiply elements

81x^2-276x^2+1=0

We add all the numbers together, and all the variables

-195x^2+1=0

a = -195; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-195)·1
Δ = 780
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:

$\sqrt{\Delta}=\sqrt{780}=\sqrt{4*195}=\sqrt{4}*\sqrt{195}=2\sqrt{195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{195}}{2*-195}=\frac{0-2\sqrt{195}}{-390}
=-\frac{2\sqrt{195}}{-390}
=-\frac{\sqrt{195}}{-195}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{195}}{2*-195}=\frac{0+2\sqrt{195}}{-390}
=\frac{2\sqrt{195}}{-390}
=\frac{\sqrt{195}}{-195}
$