1/2y-y=4+1/2y

Solution for 1/2y-y=4+1/2y equation:

1/2y-y=4+1/2y

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-1y*2y-4*2y+1-1=0

We add all the numbers together, and all the variables

-1y*2y-4*2y=0

Wy multiply elements

-2y^2-8y=0

a = -2; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-2)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-2}=\frac{0}{-4}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-2}=\frac{16}{-4}
=-4
$