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

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

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

We move all terms to the left:

6/5x-2/3-(1/6x)=0


Domain of the equation: 5x!=0

x!=0/5

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

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

We get rid of parentheses

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

We calculate fractions


(-360x^2)/270x^2+324x/270x^2+(-45x)/270x^2=0

We multiply all the terms by the denominator


(-360x^2)+324x+(-45x)=0

We get rid of parentheses

-360x^2+324x-45x=0

We add all the numbers together, and all the variables

-360x^2+279x=0

a = -360; b = 279; c = 0;
Δ = b2-4ac
Δ = 2792-4·(-360)·0
Δ = 77841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{77841}=279$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(279)-279}{2*-360}=\frac{-558}{-720}
=31/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(279)+279}{2*-360}=\frac{0}{-720}
=0
$