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

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

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

We move all terms to the left:

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


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R



Domain of the equation: 5y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-75y^2)/60y^2+40y/60y^2+(-12y)/60y^2=0

We multiply all the terms by the denominator


(-75y^2)+40y+(-12y)=0

We get rid of parentheses

-75y^2+40y-12y=0

We add all the numbers together, and all the variables

-75y^2+28y=0

a = -75; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-75)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-75}=\frac{-56}{-150}
=28/75
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-75}=\frac{0}{-150}
=0
$