1/6y-7/12y-7=1/2

Solution for 1/6y-7/12y-7=1/2 equation:

1/6y-7/12y-7=1/2

We move all terms to the left:

1/6y-7/12y-7-(1/2)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 12y!=0

y!=0/12

y!=0

y∈R


We add all the numbers together, and all the variables

1/6y-7/12y-7-(+1/2)=0

We get rid of parentheses

1/6y-7/12y-7-1/2=0

We calculate fractions


(-72y^2)/288y^2+48y/288y^2+(-168y)/288y^2-7=0

We multiply all the terms by the denominator


(-72y^2)+48y+(-168y)-7*288y^2=0

Wy multiply elements

(-72y^2)-2016y^2+48y+(-168y)=0

We get rid of parentheses

-72y^2-2016y^2+48y-168y=0

We add all the numbers together, and all the variables

-2088y^2-120y=0

a = -2088; b = -120; c = 0;
Δ = b2-4ac
Δ = -1202-4·(-2088)·0
Δ = 14400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14400}=120$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-120}{2*-2088}=\frac{0}{-4176}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+120}{2*-2088}=\frac{240}{-4176}
=-5/87
$