21/3y+2=15/y

Solution for 21/3y+2=15/y equation:

21/3y+2=15/y

We move all terms to the left:

21/3y+2-(15/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

21/3y-(+15/y)+2=0

We get rid of parentheses

21/3y-15/y+2=0

We calculate fractions


21y/3y^2+(-45y)/3y^2+2=0

We multiply all the terms by the denominator


21y+(-45y)+2*3y^2=0

Wy multiply elements

6y^2+21y+(-45y)=0

We get rid of parentheses

6y^2+21y-45y=0

We add all the numbers together, and all the variables

6y^2-24y=0

a = 6; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·6·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*6}=\frac{0}{12}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*6}=\frac{48}{12}
=4
$