y-1=1/2y+2

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

y-1=1/2y+2

We move all terms to the left:

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


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

y∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

2y^2-6y-1=0

a = 2; b = -6; c = -1;
Δ = b2-4ac
Δ = -62-4·2·(-1)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{11}}{2*2}=\frac{6-2\sqrt{11}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{11}}{2*2}=\frac{6+2\sqrt{11}}{4}
$