3/5y+2=1/2y

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

3/5y+2=1/2y

We move all terms to the left:

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

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

We get rid of parentheses

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

We calculate fractions


6y/10y^2+(-5y)/10y^2+2=0

We multiply all the terms by the denominator


6y+(-5y)+2*10y^2=0

Wy multiply elements

20y^2+6y+(-5y)=0

We get rid of parentheses

20y^2+6y-5y=0

We add all the numbers together, and all the variables

20y^2+y=0

a = 20; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·20·0
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*20}=\frac{-2}{40}
=-1/20
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*20}=\frac{0}{40}
=0
$