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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

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

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

We get rid of parentheses

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

We calculate fractions


72x^2/108x^2+(-54x)/108x^2+(-90x)/108x^2=0

We multiply all the terms by the denominator


72x^2+(-54x)+(-90x)=0

We get rid of parentheses

72x^2-54x-90x=0

We add all the numbers together, and all the variables

72x^2-144x=0

a = 72; b = -144; c = 0;
Δ = b2-4ac
Δ = -1442-4·72·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-144}{2*72}=\frac{0}{144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+144}{2*72}=\frac{288}{144}
=2
$