-y-3+2y=1/2y+1

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

-y-3+2y=1/2y+1

We move all terms to the left:

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


Domain of the equation: 2y+1)!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

y-1/2y-1-3=0

We multiply all the terms by the denominator


y*2y-1*2y-3*2y-1=0

Wy multiply elements

2y^2-2y-6y-1=0

We add all the numbers together, and all the variables

2y^2-8y-1=0

a = 2; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·2·(-1)
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6\sqrt{2}}{2*2}=\frac{8-6\sqrt{2}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6\sqrt{2}}{2*2}=\frac{8+6\sqrt{2}}{4}
$