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

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

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

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: y-2)!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

3y/2y^2+2y/2y^2+2=0

We multiply all the terms by the denominator


3y+2y+2*2y^2=0

We add all the numbers together, and all the variables

5y+2*2y^2=0

Wy multiply elements

4y^2+5y=0

a = 4; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·4·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*4}=\frac{-10}{8}
=-1+1/4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*4}=\frac{0}{8}
=0
$