2/2y-3=3/9y-5

Solution for 2/2y-3=3/9y-5 equation:

2/2y-3=3/9y-5

We move all terms to the left:

2/2y-3-(3/9y-5)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 9y-5)!=0

y∈R


We get rid of parentheses

2/2y-3/9y+5-3=0

We calculate fractions


18y/18y^2+(-6y)/18y^2+5-3=0

We add all the numbers together, and all the variables

18y/18y^2+(-6y)/18y^2+2=0

We multiply all the terms by the denominator


18y+(-6y)+2*18y^2=0

Wy multiply elements

36y^2+18y+(-6y)=0

We get rid of parentheses

36y^2+18y-6y=0

We add all the numbers together, and all the variables

36y^2+12y=0

a = 36; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·36·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*36}=\frac{-24}{72}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*36}=\frac{0}{72}
=0
$