1/2y+5=1/9y

Solution for 1/2y+5=1/9y equation:

1/2y+5=1/9y

We move all terms to the left:

1/2y+5-(1/9y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 9y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y-(+1/9y)+5=0

We get rid of parentheses

1/2y-1/9y+5=0

We calculate fractions


9y/18y^2+(-2y)/18y^2+5=0

We multiply all the terms by the denominator


9y+(-2y)+5*18y^2=0

Wy multiply elements

90y^2+9y+(-2y)=0

We get rid of parentheses

90y^2+9y-2y=0

We add all the numbers together, and all the variables

90y^2+7y=0

a = 90; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·90·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*90}=\frac{-14}{180}
=-7/90
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*90}=\frac{0}{180}
=0
$