1/4y-6=1/3y

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

1/4y-6=1/3y

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 3y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


3y/12y^2+(-4y)/12y^2-6=0

We multiply all the terms by the denominator


3y+(-4y)-6*12y^2=0

Wy multiply elements

-72y^2+3y+(-4y)=0

We get rid of parentheses

-72y^2+3y-4y=0

We add all the numbers together, and all the variables

-72y^2-1y=0

a = -72; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-72)·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*-72}=\frac{0}{-144}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-72}=\frac{2}{-144}
=-1/72
$