2/5y-1/15=5/2y

Solution for 2/5y-1/15=5/2y equation:

2/5y-1/15=5/2y

We move all terms to the left:

2/5y-1/15-(5/2y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

2/5y-(+5/2y)-1/15=0

We get rid of parentheses

2/5y-5/2y-1/15=0

We calculate fractions


(-20y^2)/150y^2+60y/150y^2+(-375y)/150y^2=0

We multiply all the terms by the denominator


(-20y^2)+60y+(-375y)=0

We get rid of parentheses

-20y^2+60y-375y=0

We add all the numbers together, and all the variables

-20y^2-315y=0

a = -20; b = -315; c = 0;
Δ = b2-4ac
Δ = -3152-4·(-20)·0
Δ = 99225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{99225}=315$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-315)-315}{2*-20}=\frac{0}{-40}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-315)+315}{2*-20}=\frac{630}{-40}
=-15+3/4
$