14/3y+5=3/y

Solution for 14/3y+5=3/y equation:

14/3y+5=3/y

We move all terms to the left:

14/3y+5-(3/y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

14/3y-(+3/y)+5=0

We get rid of parentheses

14/3y-3/y+5=0

We calculate fractions


14y/3y^2+(-9y)/3y^2+5=0

We multiply all the terms by the denominator


14y+(-9y)+5*3y^2=0

Wy multiply elements

15y^2+14y+(-9y)=0

We get rid of parentheses

15y^2+14y-9y=0

We add all the numbers together, and all the variables

15y^2+5y=0

a = 15; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·15·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*15}=\frac{-10}{30}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*15}=\frac{0}{30}
=0
$