3y/2y-1=y

Solution for 3y/2y-1=y equation:

3y/2y-1=y

We move all terms to the left:

3y/2y-1-(y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

-1y+3y/2y-1=0

We multiply all the terms by the denominator


-1y*2y+3y-1*2y=0

We add all the numbers together, and all the variables

3y-1y*2y-1*2y=0

Wy multiply elements

-2y^2+3y-2y=0

We add all the numbers together, and all the variables

-2y^2+y=0

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

$\sqrt{\Delta}=\sqrt{1}=1$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-2}=\frac{-2}{-4}
=1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-2}=\frac{0}{-4}
=0
$