1+4/y=11/(12y)

Solution for 1+4/y=11/(12y) equation:

1+4/y=11/(12y)

We move all terms to the left:

1+4/y-(11/(12y))=0


Domain of the equation: 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

4/y-(+11/12y)+1=0

We get rid of parentheses

4/y-11/12y+1=0

We calculate fractions


48y/12y^2+(-11y)/12y^2+1=0

We multiply all the terms by the denominator


48y+(-11y)+1*12y^2=0

Wy multiply elements

12y^2+48y+(-11y)=0

We get rid of parentheses

12y^2+48y-11y=0

We add all the numbers together, and all the variables

12y^2+37y=0

a = 12; b = 37; c = 0;
Δ = b2-4ac
Δ = 372-4·12·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-37}{2*12}=\frac{-74}{24}
=-3+1/12
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+37}{2*12}=\frac{0}{24}
=0
$