8y-5/5=9y/y+2

Solution for 8y-5/5=9y/y+2 equation:

8y-5/5=9y/y+2

We move all terms to the left:

8y-5/5-(9y/y+2)=0


Domain of the equation: y+2)!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

8y-9y/y-2-1=0

We multiply all the terms by the denominator


8y*y-9y-2*y-1*y=0

We add all the numbers together, and all the variables

-12y+8y*y=0

Wy multiply elements

8y^2-12y=0

a = 8; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·8·0
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*8}=\frac{0}{16}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*8}=\frac{24}{16}
=1+1/2
$