2/3y=4-5/6y

Solution for 2/3y=4-5/6y equation:

2/3y=4-5/6y

We move all terms to the left:

2/3y-(4-5/6y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 6y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2/3y-(-5/6y+4)=0

We get rid of parentheses

2/3y+5/6y-4=0

We calculate fractions


12y/18y^2+15y/18y^2-4=0

We multiply all the terms by the denominator


12y+15y-4*18y^2=0

We add all the numbers together, and all the variables

27y-4*18y^2=0

Wy multiply elements

-72y^2+27y=0

a = -72; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-72)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-72}=\frac{-54}{-144}
=3/8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-72}=\frac{0}{-144}
=0
$