108+2/3x=X

Solution for 108+2/3x=X equation:

108+2/3x=x

We move all terms to the left:

108+2/3x-(x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+2/3x+108=0

We multiply all the terms by the denominator


-1x*3x+108*3x+2=0

Wy multiply elements

-3x^2+324x+2=0

a = -3; b = 324; c = +2;
Δ = b2-4ac
Δ = 3242-4·(-3)·2
Δ = 105000
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:

$\sqrt{\Delta}=\sqrt{105000}=\sqrt{2500*42}=\sqrt{2500}*\sqrt{42}=50\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-50\sqrt{42}}{2*-3}=\frac{-324-50\sqrt{42}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+50\sqrt{42}}{2*-3}=\frac{-324+50\sqrt{42}}{-6}
$