6/x+2/3x=2

Solution for 6/x+2/3x=2 equation:

6/x+2/3x=2

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We calculate fractions


18x/3x^2+2x/3x^2-2=0

We multiply all the terms by the denominator


18x+2x-2*3x^2=0

We add all the numbers together, and all the variables

20x-2*3x^2=0

Wy multiply elements

-6x^2+20x=0

a = -6; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-6)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-6}=\frac{-40}{-12}
=3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-6}=\frac{0}{-12}
=0
$