1-2/(6y)=3/(12y)

Solution for 1-2/(6y)=3/(12y) equation:

1-2/(6y)=3/(12y)

We move all terms to the left:

1-2/(6y)-(3/(12y))=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 12y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

-2/6y-(+3/12y)+1=0

We get rid of parentheses

-2/6y-3/12y+1=0

We calculate fractions


(-24y)/72y^2+(-18y)/72y^2+1=0

We multiply all the terms by the denominator


(-24y)+(-18y)+1*72y^2=0

Wy multiply elements

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

We get rid of parentheses

72y^2-24y-18y=0

We add all the numbers together, and all the variables

72y^2-42y=0

a = 72; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·72·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*72}=\frac{0}{144}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*72}=\frac{84}{144}
=7/12
$