4+2*1/2y=2y+4

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

4+2*1/2y=2y+4

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-4y^2-8y+8y+2=0

We add all the numbers together, and all the variables

-4y^2+2=0

a = -4; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-4)·2
Δ = 32
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:

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