1/3y+2=2/15y

Solution for 1/3y+2=2/15y equation:

1/3y+2=2/15y

We move all terms to the left:

1/3y+2-(2/15y)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 15y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/3y-(+2/15y)+2=0

We get rid of parentheses

1/3y-2/15y+2=0

We calculate fractions


15y/45y^2+(-6y)/45y^2+2=0

We multiply all the terms by the denominator


15y+(-6y)+2*45y^2=0

Wy multiply elements

90y^2+15y+(-6y)=0

We get rid of parentheses

90y^2+15y-6y=0

We add all the numbers together, and all the variables

90y^2+9y=0

a = 90; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·90·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*90}=\frac{-18}{180}
=-1/10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*90}=\frac{0}{180}
=0
$