8/y-2=12/2y-8

Solution for 8/y-2=12/2y-8 equation:

8/y-2=12/2y-8

We move all terms to the left:

8/y-2-(12/2y-8)=0


Domain of the equation: y!=0

y∈R



Domain of the equation: 2y-8)!=0

y∈R


We get rid of parentheses

8/y-12/2y+8-2=0

We calculate fractions


16y/2y^2+(-12y)/2y^2+8-2=0

We add all the numbers together, and all the variables

16y/2y^2+(-12y)/2y^2+6=0

We multiply all the terms by the denominator


16y+(-12y)+6*2y^2=0

Wy multiply elements

12y^2+16y+(-12y)=0

We get rid of parentheses

12y^2+16y-12y=0

We add all the numbers together, and all the variables

12y^2+4y=0

a = 12; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·12·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*12}=\frac{-8}{24}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*12}=\frac{0}{24}
=0
$