15/y=21/3y+2

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

15/y=21/3y+2

We move all terms to the left:

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


Domain of the equation: y!=0

y∈R



Domain of the equation: 3y+2)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We get rid of parentheses

-6y^2+45y-21y=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{-48}{-12}
=+4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-6}=\frac{0}{-12}
=0
$