8/2y-1=3/1+y

Solution for 8/2y-1=3/1+y equation:

8/2y-1=3/1+y

We move all terms to the left:

8/2y-1-(3/1+y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 1+y)!=0

We move all terms containing y to the left, all other terms to the right

y)!=-1

y!=-1/1

y!=-1

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

8/2y-y-1=0

We multiply all the terms by the denominator


-y*2y-1*2y+8=0

Wy multiply elements

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

a = -2; b = -2; c = +8;
Δ = b2-4ac
Δ = -22-4·(-2)·8
Δ = 68
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{17}}{2*-2}=\frac{2-2\sqrt{17}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{17}}{2*-2}=\frac{2+2\sqrt{17}}{-4}
$