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

Wy multiply elements

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

We get rid of parentheses

162x^2+6x-27x-24x=0

We add all the numbers together, and all the variables

162x^2-45x=0

a = 162; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·162·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*162}=\frac{0}{324}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*162}=\frac{90}{324}
=5/18
$