(1/y-1)+(1/20)=-4/5y-5

Solution for (1/y-1)+(1/20)=-4/5y-5 equation:

(1/y-1)+(1/20)=-4/5y-5

We move all terms to the left:

(1/y-1)+(1/20)-(-4/5y-5)=0


Domain of the equation: y-1)!=0

y∈R



Domain of the equation: 5y-5)!=0

y∈R


We add all the numbers together, and all the variables

(1/y-1)-(-4/5y-5)+(+1/20)=0

We get rid of parentheses

1/y+4/5y-1+5+1/20=0

We calculate fractions


25y^2/200y^2+200y/200y^2+160y/200y^2-1+5=0

We add all the numbers together, and all the variables

25y^2/200y^2+200y/200y^2+160y/200y^2+4=0

We multiply all the terms by the denominator


25y^2+200y+160y+4*200y^2=0

We add all the numbers together, and all the variables

25y^2+360y+4*200y^2=0

Wy multiply elements

25y^2+800y^2+360y=0

We add all the numbers together, and all the variables

825y^2+360y=0

a = 825; b = 360; c = 0;
Δ = b2-4ac
Δ = 3602-4·825·0
Δ = 129600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{129600}=360$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-360}{2*825}=\frac{-720}{1650}
=-24/55
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+360}{2*825}=\frac{0}{1650}
=0
$