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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-4y^2+16y=0

a = -4; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-4)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*-4}=\frac{-32}{-8}
=+4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*-4}=\frac{0}{-8}
=0
$