8/2y-3=6/y+4

Solution for 8/2y-3=6/y+4 equation:

8/2y-3=6/y+4

We move all terms to the left:

8/2y-3-(6/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-6/y-4-3=0

We calculate fractions


8y/2y^2+(-12y)/2y^2-4-3=0

We add all the numbers together, and all the variables

8y/2y^2+(-12y)/2y^2-7=0

We multiply all the terms by the denominator


8y+(-12y)-7*2y^2=0

Wy multiply elements

-14y^2+8y+(-12y)=0

We get rid of parentheses

-14y^2+8y-12y=0

We add all the numbers together, and all the variables

-14y^2-4y=0

a = -14; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-14)·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*-14}=\frac{0}{-28}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-14}=\frac{8}{-28}
=-2/7
$