(-1/2y+8)+2=6/y+4

Solution for (-1/2y+8)+2=6/y+4 equation:

(-1/2y+8)+2=6/y+4

We move all terms to the left:

(-1/2y+8)+2-(6/y+4)=0


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

y∈R



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

y∈R


We get rid of parentheses

-1/2y-6/y+8-4+2=0

We calculate fractions


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

We add all the numbers together, and all the variables

(-1y)/2y^2+(-12y)/2y^2+8-4+2=0

We add all the numbers together, and all the variables

(-1y)/2y^2+(-12y)/2y^2+6=0

We multiply all the terms by the denominator


(-1y)+(-12y)+6*2y^2=0

Wy multiply elements

12y^2+(-1y)+(-12y)=0

We get rid of parentheses

12y^2-1y-12y=0

We add all the numbers together, and all the variables

12y^2-13y=0

a = 12; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·12·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*12}=\frac{0}{24}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*12}=\frac{26}{24}
=1+1/12
$