1/2y+4=1/10y

Solution for 1/2y+4=1/10y equation:

1/2y+4=1/10y

We move all terms to the left:

1/2y+4-(1/10y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 10y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y-(+1/10y)+4=0

We get rid of parentheses

1/2y-1/10y+4=0

We calculate fractions


10y/20y^2+(-2y)/20y^2+4=0

We multiply all the terms by the denominator


10y+(-2y)+4*20y^2=0

Wy multiply elements

80y^2+10y+(-2y)=0

We get rid of parentheses

80y^2+10y-2y=0

We add all the numbers together, and all the variables

80y^2+8y=0

a = 80; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·80·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*80}=\frac{-16}{160}
=-1/10
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*80}=\frac{0}{160}
=0
$