3/3y-6=1/4y

Solution for 3/3y-6=1/4y equation:

3/3y-6=1/4y

We move all terms to the left:

3/3y-6-(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

3/3y-(+1/4y)-6=0

We get rid of parentheses

3/3y-1/4y-6=0

We calculate fractions


12y/12y^2+(-3y)/12y^2-6=0

We multiply all the terms by the denominator


12y+(-3y)-6*12y^2=0

Wy multiply elements

-72y^2+12y+(-3y)=0

We get rid of parentheses

-72y^2+12y-3y=0

We add all the numbers together, and all the variables

-72y^2+9y=0

a = -72; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-72)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-72}=\frac{-18}{-144}
=1/8
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-72}=\frac{0}{-144}
=0
$