3+1/2y=y

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

3+1/2y=y

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-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}
$