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

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

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

We move all terms to the left:

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


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


54y^2/72y^2+(-60y)/72y^2+(-48y)/72y^2=0

We multiply all the terms by the denominator


54y^2+(-60y)+(-48y)=0

We get rid of parentheses

54y^2-60y-48y=0

We add all the numbers together, and all the variables

54y^2-108y=0

a = 54; b = -108; c = 0;
Δ = b2-4ac
Δ = -1082-4·54·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-108}{2*54}=\frac{0}{108}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+108}{2*54}=\frac{216}{108}
=2
$