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

Solution for 1/x-2+3/x=2/3x equation:

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(9x+1)/3x^2+(-2x)/3x^2-2=0

We multiply all the terms by the denominator


(9x+1)+(-2x)-2*3x^2=0

Wy multiply elements

-6x^2+(9x+1)+(-2x)=0

We get rid of parentheses

-6x^2+9x-2x+1=0

We add all the numbers together, and all the variables

-6x^2+7x+1=0

a = -6; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-6)·1
Δ = 73
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{73}}{2*-6}=\frac{-7-\sqrt{73}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{73}}{2*-6}=\frac{-7+\sqrt{73}}{-12}
$