-2/3x+1=4-1/6x

Solution for -2/3x+1=4-1/6x equation:

-2/3x+1=4-1/6x

We move all terms to the left:

-2/3x+1-(4-1/6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-2/3x-(-1/6x+4)+1=0

We get rid of parentheses

-2/3x+1/6x-4+1=0

We calculate fractions


(-12x)/18x^2+3x/18x^2-4+1=0

We add all the numbers together, and all the variables

(-12x)/18x^2+3x/18x^2-3=0

We multiply all the terms by the denominator


(-12x)+3x-3*18x^2=0

We add all the numbers together, and all the variables

3x+(-12x)-3*18x^2=0

Wy multiply elements

-54x^2+3x+(-12x)=0

We get rid of parentheses

-54x^2+3x-12x=0

We add all the numbers together, and all the variables

-54x^2-9x=0

a = -54; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-54)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-54}=\frac{0}{-108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-54}=\frac{18}{-108}
=-1/6
$