3/4y+6=4/12y+4

Solution for 3/4y+6=4/12y+4 equation:

3/4y+6=4/12y+4

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R



Domain of the equation: 12y+4)!=0

y∈R


We get rid of parentheses

3/4y-4/12y-4+6=0

We calculate fractions


36y/48y^2+(-16y)/48y^2-4+6=0

We add all the numbers together, and all the variables

36y/48y^2+(-16y)/48y^2+2=0

We multiply all the terms by the denominator


36y+(-16y)+2*48y^2=0

Wy multiply elements

96y^2+36y+(-16y)=0

We get rid of parentheses

96y^2+36y-16y=0

We add all the numbers together, and all the variables

96y^2+20y=0

a = 96; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·96·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*96}=\frac{-40}{192}
=-5/24
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*96}=\frac{0}{192}
=0
$