2y-2=1/2y+4

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

2y-2=1/2y+4

We move all terms to the left:

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


Domain of the equation: 2y+4)!=0

y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4y^2-8y-4y-1=0

We add all the numbers together, and all the variables

4y^2-12y-1=0

a = 4; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·4·(-1)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{10}}{2*4}=\frac{12-4\sqrt{10}}{8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{10}}{2*4}=\frac{12+4\sqrt{10}}{8}
$