1/6y+4=2/3y+8

Solution for 1/6y+4=2/3y+8 equation:

1/6y+4=2/3y+8

We move all terms to the left:

1/6y+4-(2/3y+8)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 3y+8)!=0

y∈R


We get rid of parentheses

1/6y-2/3y-8+4=0

We calculate fractions


3y/18y^2+(-12y)/18y^2-8+4=0

We add all the numbers together, and all the variables

3y/18y^2+(-12y)/18y^2-4=0

We multiply all the terms by the denominator


3y+(-12y)-4*18y^2=0

Wy multiply elements

-72y^2+3y+(-12y)=0

We get rid of parentheses

-72y^2+3y-12y=0

We add all the numbers together, and all the variables

-72y^2-9y=0

a = -72; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-72)·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*-72}=\frac{0}{-144}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-72}=\frac{18}{-144}
=-1/8
$