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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


6x/162x^2+27x/162x^2+(-24x)/162x^2+1=0

We multiply all the terms by the denominator


6x+27x+(-24x)+1*162x^2=0

We add all the numbers together, and all the variables

33x+(-24x)+1*162x^2=0

Wy multiply elements

162x^2+33x+(-24x)=0

We get rid of parentheses

162x^2+33x-24x=0

We add all the numbers together, and all the variables

162x^2+9x=0

a = 162; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·162·0
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*162}=\frac{-18}{324}
=-1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*162}=\frac{0}{324}
=0
$