3/2y-2=4+2/4y

Solution for 3/2y-2=4+2/4y equation:

3/2y-2=4+2/4y

We move all terms to the left:

3/2y-2-(4+2/4y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 4y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

3/2y-(2/4y+4)-2=0

We get rid of parentheses

3/2y-2/4y-4-2=0

We calculate fractions


12y/8y^2+(-4y)/8y^2-4-2=0

We add all the numbers together, and all the variables

12y/8y^2+(-4y)/8y^2-6=0

We multiply all the terms by the denominator


12y+(-4y)-6*8y^2=0

Wy multiply elements

-48y^2+12y+(-4y)=0

We get rid of parentheses

-48y^2+12y-4y=0

We add all the numbers together, and all the variables

-48y^2+8y=0

a = -48; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-48)·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*-48}=\frac{-16}{-96}
=1/6
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-48}=\frac{0}{-96}
=0
$