3/2y+-y=4+1/2y

Solution for 3/2y+-y=4+1/2y equation:

3/2y+-y=4+1/2y

We move all terms to the left:

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


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R



Domain of the equation: 2y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-1y*2y-4*2y+3-1=0

We add all the numbers together, and all the variables

-1y*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 = 80
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:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{5}}{2*-2}=\frac{8-4\sqrt{5}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{5}}{2*-2}=\frac{8+4\sqrt{5}}{-4}
$