2x-(2/3x)=6

Solution for 2x-(2/3x)=6 equation:

2x-(2/3x)=6

We move all terms to the left:

2x-(2/3x)-(6)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+2/3x)-6=0

We get rid of parentheses

2x-2/3x-6=0

We multiply all the terms by the denominator


2x*3x-6*3x-2=0

Wy multiply elements

6x^2-18x-2=0

a = 6; b = -18; c = -2;
Δ = b2-4ac
Δ = -182-4·6·(-2)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*6}=\frac{18-2\sqrt{93}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*6}=\frac{18+2\sqrt{93}}{12}
$