1/3y-9=1/4y

Solution for 1/3y-9=1/4y equation:

1/3y-9=1/4y

We move all terms to the left:

1/3y-9-(1/4y)=0


Domain of the equation: 3y!=0

y!=0/3

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

1/3y-(+1/4y)-9=0

We get rid of parentheses

1/3y-1/4y-9=0

We calculate fractions


4y/12y^2+(-3y)/12y^2-9=0

We multiply all the terms by the denominator


4y+(-3y)-9*12y^2=0

Wy multiply elements

-108y^2+4y+(-3y)=0

We get rid of parentheses

-108y^2+4y-3y=0

We add all the numbers together, and all the variables

-108y^2+y=0

a = -108; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-108)·0
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{-(1)-1}{2*-108}=\frac{-2}{-216}
=1/108
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-108}=\frac{0}{-216}
=0
$