6/y-5=18/y1+1

Solution for 6/y-5=18/y1+1 equation:

6/y-5=18/y1+1

We move all terms to the left:

6/y-5-(18/y1+1)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: y1+1)!=0

y∈R


We get rid of parentheses

6/y-18/y1-1-5=0

We calculate fractions


6y/y^2+(-18y)/y^2-1-5=0

We add all the numbers together, and all the variables

6y/y^2+(-18y)/y^2-6=0

We multiply all the terms by the denominator


6y+(-18y)-6*y^2=0

We add all the numbers together, and all the variables

-6y^2+6y+(-18y)=0

We get rid of parentheses

-6y^2+6y-18y=0

We add all the numbers together, and all the variables

-6y^2-12y=0

a = -6; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-6)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-6}=\frac{0}{-12}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-6}=\frac{24}{-12}
=-2
$