3/2x-x=4+0.5x

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

3/2x-x=4+0.5x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

Wy multiply elements

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

We add all the numbers together, and all the variables

-3x^2-8x+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:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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