2/5y-3=1/3y

Solution for 2/5y-3=1/3y equation:

2/5y-3=1/3y

We move all terms to the left:

2/5y-3-(1/3y)=0


Domain of the equation: 5y!=0

y!=0/5

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

2/5y-(+1/3y)-3=0

We get rid of parentheses

2/5y-1/3y-3=0

We calculate fractions


6y/15y^2+(-5y)/15y^2-3=0

We multiply all the terms by the denominator


6y+(-5y)-3*15y^2=0

Wy multiply elements

-45y^2+6y+(-5y)=0

We get rid of parentheses

-45y^2+6y-5y=0

We add all the numbers together, and all the variables

-45y^2+y=0

a = -45; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-45)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-45}=\frac{-2}{-90}
=1/45
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-45}=\frac{0}{-90}
=0
$