2/6y+4=3/12y-6

Solution for 2/6y+4=3/12y-6 equation:

2/6y+4=3/12y-6

We move all terms to the left:

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


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 12y-6)!=0

y∈R


We get rid of parentheses

2/6y-3/12y+6+4=0

We calculate fractions


24y/72y^2+(-18y)/72y^2+6+4=0

We add all the numbers together, and all the variables

24y/72y^2+(-18y)/72y^2+10=0

We multiply all the terms by the denominator


24y+(-18y)+10*72y^2=0

Wy multiply elements

720y^2+24y+(-18y)=0

We get rid of parentheses

720y^2+24y-18y=0

We add all the numbers together, and all the variables

720y^2+6y=0

a = 720; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·720·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*720}=\frac{-12}{1440}
=-1/120
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*720}=\frac{0}{1440}
=0
$