3/2y-y=4+0.5y

Solution for 3/2y-y=4+0.5y equation:

3/2y-y=4+0.5y

We move all terms to the left:

3/2y-y-(4+0.5y)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

3/2y-y-(0.5y+4)=0

We add all the numbers together, and all the variables

-1y+3/2y-(0.5y+4)=0

We get rid of parentheses

-1y+3/2y-0.5y-4=0

We multiply all the terms by the denominator


-1y*2y-(0.5y)*2y-4*2y+3=0

We add all the numbers together, and all the variables

-1y*2y-(+0.5y)*2y-4*2y+3=0

We multiply parentheses

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

Wy multiply elements

-0y^2-2y^2-8y+3=0

We add all the numbers together, and all the variables

-3y^2-8y+3=0

a = -3; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-3)·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-10}{2*-3}=\frac{-2}{-6}
=1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+10}{2*-3}=\frac{18}{-6}
=-3
$