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

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

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

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-576y^2)/108y^2+54y/108y^2+18y/108y^2=0

We multiply all the terms by the denominator


(-576y^2)+54y+18y=0

We add all the numbers together, and all the variables

(-576y^2)+72y=0

We get rid of parentheses

-576y^2+72y=0

a = -576; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·(-576)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*-576}=\frac{-144}{-1152}
=1/8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*-576}=\frac{0}{-1152}
=0
$