3-y=2/y

Solution for 3-y=2/y equation:

3-y=2/y

We move all terms to the left:

3-y-(2/y)=0


Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-1y-2/y+3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3y-1y*y-2=0

Wy multiply elements

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

a = -1; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·(-1)·(-2)
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{-(3)-1}{2*-1}=\frac{-4}{-2}
=+2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+1}{2*-1}=\frac{-2}{-2}
=1
$