x(1/3x)=108

Solution for x(1/3x)=108 equation:

x(1/3x)=108

We move all terms to the left:

x(1/3x)-(108)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x(+1/3x)-108=0

We multiply parentheses

x^2-108=0

a = 1; b = 0; c = -108;
Δ = b2-4ac
Δ = 02-4·1·(-108)
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*1}=\frac{0-12\sqrt{3}}{2}
=-\frac{12\sqrt{3}}{2}
=-6\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*1}=\frac{0+12\sqrt{3}}{2}
=\frac{12\sqrt{3}}{2}
=6\sqrt{3}
$