2/3y-5/6=1/2y-4

Solution for 2/3y-5/6=1/2y-4 equation:

2/3y-5/6=1/2y-4

We move all terms to the left:

2/3y-5/6-(1/2y-4)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 2y-4)!=0

y∈R


We get rid of parentheses

2/3y-1/2y+4-5/6=0

We calculate fractions


(-60y^2)/216y^2+144y/216y^2+(-108y)/216y^2+4=0

We multiply all the terms by the denominator


(-60y^2)+144y+(-108y)+4*216y^2=0

Wy multiply elements

(-60y^2)+864y^2+144y+(-108y)=0

We get rid of parentheses

-60y^2+864y^2+144y-108y=0

We add all the numbers together, and all the variables

804y^2+36y=0

a = 804; b = 36; c = 0;
Δ = b2-4ac
Δ = 362-4·804·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-36}{2*804}=\frac{-72}{1608}
=-3/67
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+36}{2*804}=\frac{0}{1608}
=0
$