-8/2y-8=5/y+4

Solution for -8/2y-8=5/y+4 equation:

-8/2y-8=5/y+4

We move all terms to the left:

-8/2y-8-(5/y+4)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: y+4)!=0

y∈R


We get rid of parentheses

-8/2y-5/y-4-8=0

We calculate fractions


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

We add all the numbers together, and all the variables

(-8y)/2y^2+(-10y)/2y^2-12=0

We multiply all the terms by the denominator


(-8y)+(-10y)-12*2y^2=0

Wy multiply elements

-24y^2+(-8y)+(-10y)=0

We get rid of parentheses

-24y^2-8y-10y=0

We add all the numbers together, and all the variables

-24y^2-18y=0

a = -24; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-24)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-24}=\frac{0}{-48}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-24}=\frac{36}{-48}
=-3/4
$