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

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

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

We move all terms to the left:

1/5x+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

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

We get rid of parentheses

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

We calculate fractions


360x^2/270x^2+54x/270x^2+(-45x)/270x^2=0

We multiply all the terms by the denominator


360x^2+54x+(-45x)=0

We get rid of parentheses

360x^2+54x-45x=0

We add all the numbers together, and all the variables

360x^2+9x=0

a = 360; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·360·0
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*360}=\frac{-18}{720}
=-1/40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*360}=\frac{0}{720}
=0
$