y/2y=8+y

Solution for y/2y=8+y equation:

y/2y=8+y

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

y/2y-y-8=0

We multiply all the terms by the denominator


y-y*2y-8*2y=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-2y^2-15y=0

a = -2; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-2)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-2}=\frac{0}{-4}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-2}=\frac{30}{-4}
=-7+1/2
$