8y/8y+8+9y+1/2y+2=9y+4/y+1

Solution for 8y/8y+8+9y+1/2y+2=9y+4/y+1 equation:

8y/8y+8+9y+1/2y+2=9y+4/y+1

We move all terms to the left:

8y/8y+8+9y+1/2y+2-(9y+4/y+1)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



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

y∈R


We add all the numbers together, and all the variables

9y+8y/8y+1/2y-(9y+4/y+1)+10=0

We get rid of parentheses

9y+8y/8y+1/2y-9y-4/y-1+10=0

Fractions to decimals

1/2y-4/y+9y-9y-1+10+1=0

We calculate fractions


9y-9y+y/2y^2+(-8y)/2y^2-1+10+1=0

We add all the numbers together, and all the variables

y/2y^2+(-8y)/2y^2+10=0

We multiply all the terms by the denominator


y+(-8y)+10*2y^2=0

Wy multiply elements

20y^2+y+(-8y)=0

We get rid of parentheses

20y^2+y-8y=0

We add all the numbers together, and all the variables

20y^2-7y=0

a = 20; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·20·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*20}=\frac{0}{40}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*20}=\frac{14}{40}
=7/20
$