3/5y-2/7=3/8y

Solution for 3/5y-2/7=3/8y equation:

3/5y-2/7=3/8y

We move all terms to the left:

3/5y-2/7-(3/8y)=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R



Domain of the equation: 8y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3/5y-(+3/8y)-2/7=0

We get rid of parentheses

3/5y-3/8y-2/7=0

We calculate fractions


(-640y^2)/1960y^2+1176y/1960y^2+(-735y)/1960y^2=0

We multiply all the terms by the denominator


(-640y^2)+1176y+(-735y)=0

We get rid of parentheses

-640y^2+1176y-735y=0

We add all the numbers together, and all the variables

-640y^2+441y=0

a = -640; b = 441; c = 0;
Δ = b2-4ac
Δ = 4412-4·(-640)·0
Δ = 194481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{194481}=441$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(441)-441}{2*-640}=\frac{-882}{-1280}
=441/640
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(441)+441}{2*-640}=\frac{0}{-1280}
=0
$