2x/3x-4-1/x=2/3

Solution for 2x/3x-4-1/x=2/3 equation:

2x/3x-4-1/x=2/3

We move all terms to the left:

2x/3x-4-1/x-(2/3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x/3x-1/x-4-(+2/3)=0

We get rid of parentheses

2x/3x-1/x-4-2/3=0

We calculate fractions


2x^2/27x^2+(-27x)/27x^2+(-2x)/27x^2-4=0

We multiply all the terms by the denominator


2x^2+(-27x)+(-2x)-4*27x^2=0

Wy multiply elements

2x^2-108x^2+(-27x)+(-2x)=0

We get rid of parentheses

2x^2-108x^2-27x-2x=0

We add all the numbers together, and all the variables

-106x^2-29x=0

a = -106; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·(-106)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*-106}=\frac{0}{-212}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*-106}=\frac{58}{-212}
=-29/106
$