7+2/3y=1/6y-5

Solution for 7+2/3y=1/6y-5 equation:

7+2/3y=1/6y-5

We move all terms to the left:

7+2/3y-(1/6y-5)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 6y-5)!=0

y∈R


We get rid of parentheses

2/3y-1/6y+5+7=0

We calculate fractions


12y/18y^2+(-3y)/18y^2+5+7=0

We add all the numbers together, and all the variables

12y/18y^2+(-3y)/18y^2+12=0

We multiply all the terms by the denominator


12y+(-3y)+12*18y^2=0

Wy multiply elements

216y^2+12y+(-3y)=0

We get rid of parentheses

216y^2+12y-3y=0

We add all the numbers together, and all the variables

216y^2+9y=0

a = 216; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·216·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*216}=\frac{-18}{432}
=-1/24
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*216}=\frac{0}{432}
=0
$