2+4/y=7/(12y)

Solution for 2+4/y=7/(12y) equation:

2+4/y=7/(12y)

We move all terms to the left:

2+4/y-(7/(12y))=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 12y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

4/y-(+7/12y)+2=0

We get rid of parentheses

4/y-7/12y+2=0

We calculate fractions


48y/12y^2+(-7y)/12y^2+2=0

We multiply all the terms by the denominator


48y+(-7y)+2*12y^2=0

Wy multiply elements

24y^2+48y+(-7y)=0

We get rid of parentheses

24y^2+48y-7y=0

We add all the numbers together, and all the variables

24y^2+41y=0

a = 24; b = 41; c = 0;
Δ = b2-4ac
Δ = 412-4·24·0
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-41}{2*24}=\frac{-82}{48}
=-1+17/24
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+41}{2*24}=\frac{0}{48}
=0
$