12-1/3y+4=1/4y

Solution for 12-1/3y+4=1/4y equation:

12-1/3y+4=1/4y

We move all terms to the left:

12-1/3y+4-(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)+12+4=0

We add all the numbers together, and all the variables

-1/3y-(+1/4y)+16=0

We get rid of parentheses

-1/3y-1/4y+16=0

We calculate fractions


(-4y)/12y^2+(-3y)/12y^2+16=0

We multiply all the terms by the denominator


(-4y)+(-3y)+16*12y^2=0

Wy multiply elements

192y^2+(-4y)+(-3y)=0

We get rid of parentheses

192y^2-4y-3y=0

We add all the numbers together, and all the variables

192y^2-7y=0

a = 192; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·192·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*192}=\frac{0}{384}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*192}=\frac{14}{384}
=7/192
$