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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

-2x^2-8x-4x+2=0

We add all the numbers together, and all the variables

-2x^2-12x+2=0

a = -2; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·(-2)·2
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{10}}{2*-2}=\frac{12-4\sqrt{10}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{10}}{2*-2}=\frac{12+4\sqrt{10}}{-4}
$