2/3x-5=1/6x-1

Solution for 2/3x-5=1/6x-1 equation:

2/3x-5=1/6x-1

We move all terms to the left:

2/3x-5-(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

2/3x-1/6x+1-5=0

We calculate fractions


12x/18x^2+(-3x)/18x^2+1-5=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-72x^2+12x+(-3x)=0

We get rid of parentheses

-72x^2+12x-3x=0

We add all the numbers together, and all the variables

-72x^2+9x=0

a = -72; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-72)·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*-72}=\frac{-18}{-144}
=1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-72}=\frac{0}{-144}
=0
$