6/2y-4=-3/y

Solution for 6/2y-4=-3/y equation:

6/2y-4=-3/y

We move all terms to the left:

6/2y-4-(-3/y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: y)!=0

y!=0/1

y!=0

y∈R


We get rid of parentheses

6/2y+3/y-4=0

We calculate fractions


6y/2y^2+6y/2y^2-4=0

We multiply all the terms by the denominator


6y+6y-4*2y^2=0

We add all the numbers together, and all the variables

12y-4*2y^2=0

Wy multiply elements

-8y^2+12y=0

a = -8; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-8)·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*-8}=\frac{-24}{-16}
=1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-8}=\frac{0}{-16}
=0
$