5/12y+1=1/6y+7

Solution for 5/12y+1=1/6y+7 equation:

5/12y+1=1/6y+7

We move all terms to the left:

5/12y+1-(1/6y+7)=0


Domain of the equation: 12y!=0

y!=0/12

y!=0

y∈R



Domain of the equation: 6y+7)!=0

y∈R


We get rid of parentheses

5/12y-1/6y-7+1=0

We calculate fractions


30y/72y^2+(-12y)/72y^2-7+1=0

We add all the numbers together, and all the variables

30y/72y^2+(-12y)/72y^2-6=0

We multiply all the terms by the denominator


30y+(-12y)-6*72y^2=0

Wy multiply elements

-432y^2+30y+(-12y)=0

We get rid of parentheses

-432y^2+30y-12y=0

We add all the numbers together, and all the variables

-432y^2+18y=0

a = -432; b = 18; c = 0;
Δ = b2-4ac
Δ = 182-4·(-432)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-18}{2*-432}=\frac{-36}{-864}
=1/24
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+18}{2*-432}=\frac{0}{-864}
=0
$