y+2/2y-1=3

Solution for y+2/2y-1=3 equation:

y+2/2y-1=3

We move all terms to the left:

y+2/2y-1-(3)=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+2/2y-4=0

We multiply all the terms by the denominator


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

Wy multiply elements

2y^2-8y+2=0

a = 2; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·2·2
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{3}}{2*2}=\frac{8-4\sqrt{3}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{3}}{2*2}=\frac{8+4\sqrt{3}}{4}
$