1/2y+9=1/10y

Solution for 1/2y+9=1/10y equation:

1/2y+9=1/10y

We move all terms to the left:

1/2y+9-(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)+9=0

We get rid of parentheses

1/2y-1/10y+9=0

We calculate fractions


10y/20y^2+(-2y)/20y^2+9=0

We multiply all the terms by the denominator


10y+(-2y)+9*20y^2=0

Wy multiply elements

180y^2+10y+(-2y)=0

We get rid of parentheses

180y^2+10y-2y=0

We add all the numbers together, and all the variables

180y^2+8y=0

a = 180; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·180·0
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*180}=\frac{-16}{360}
=-2/45
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*180}=\frac{0}{360}
=0
$