1/6y-1/3=10/12y+1

Solution for 1/6y-1/3=10/12y+1 equation:

1/6y-1/3=10/12y+1

We move all terms to the left:

1/6y-1/3-(10/12y+1)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 12y+1)!=0

y∈R


We get rid of parentheses

1/6y-10/12y-1-1/3=0

We calculate fractions


(-72y^2)/648y^2+108y/648y^2+(-540y)/648y^2-1=0

We multiply all the terms by the denominator


(-72y^2)+108y+(-540y)-1*648y^2=0

Wy multiply elements

(-72y^2)-648y^2+108y+(-540y)=0

We get rid of parentheses

-72y^2-648y^2+108y-540y=0

We add all the numbers together, and all the variables

-720y^2-432y=0

a = -720; b = -432; c = 0;
Δ = b2-4ac
Δ = -4322-4·(-720)·0
Δ = 186624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{186624}=432$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-432)-432}{2*-720}=\frac{0}{-1440}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-432)+432}{2*-720}=\frac{864}{-1440}
=-3/5
$