8/y+3=4/3y

Solution for 8/y+3=4/3y equation:

8/y+3=4/3y

We move all terms to the left:

8/y+3-(4/3y)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

8/y-(+4/3y)+3=0

We get rid of parentheses

8/y-4/3y+3=0

We calculate fractions


24y/3y^2+(-4y)/3y^2+3=0

We multiply all the terms by the denominator


24y+(-4y)+3*3y^2=0

Wy multiply elements

9y^2+24y+(-4y)=0

We get rid of parentheses

9y^2+24y-4y=0

We add all the numbers together, and all the variables

9y^2+20y=0

a = 9; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·9·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*9}=\frac{-40}{18}
=-2+2/9
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*9}=\frac{0}{18}
=0
$