4/y-5-8/2y+6+2/y-5=0

Solution for 4/y-5-8/2y+6+2/y-5=0 equation:

4/y-5-8/2y+6+2/y-5=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

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

We calculate fractions


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

We multiply all the terms by the denominator


(4y+4)+(-8y)-4*2y^2=0

Wy multiply elements

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

We get rid of parentheses

-8y^2+4y-8y+4=0

We add all the numbers together, and all the variables

-8y^2-4y+4=0

a = -8; b = -4; c = +4;
Δ = b2-4ac
Δ = -42-4·(-8)·4
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{-(-4)-12}{2*-8}=\frac{-8}{-16}
=1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+12}{2*-8}=\frac{16}{-16}
=-1
$