5/8y=2/5y+3

Solution for 5/8y=2/5y+3 equation:

5/8y=2/5y+3

We move all terms to the left:

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


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R



Domain of the equation: 5y+3)!=0

y∈R


We get rid of parentheses

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

We calculate fractions


25y/40y^2+(-16y)/40y^2-3=0

We multiply all the terms by the denominator


25y+(-16y)-3*40y^2=0

Wy multiply elements

-120y^2+25y+(-16y)=0

We get rid of parentheses

-120y^2+25y-16y=0

We add all the numbers together, and all the variables

-120y^2+9y=0

a = -120; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-120)·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*-120}=\frac{-18}{-240}
=3/40
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-120}=\frac{0}{-240}
=0
$