1/2y+1=1/5y

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

1/2y+1=1/5y

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

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

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

We get rid of parentheses

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

We calculate fractions


5y/10y^2+(-2y)/10y^2+1=0

We multiply all the terms by the denominator


5y+(-2y)+1*10y^2=0

Wy multiply elements

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

We get rid of parentheses

10y^2+5y-2y=0

We add all the numbers together, and all the variables

10y^2+3y=0

a = 10; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·10·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*10}=\frac{-6}{20}
=-3/10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*10}=\frac{0}{20}
=0
$