1/2x-x=6+3/2x

Solution for 1/2x-x=6+3/2x equation:

1/2x-x=6+3/2x

We move all terms to the left:

1/2x-x-(6+3/2x)=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

1/2x-x-(3/2x+6)=0

We add all the numbers together, and all the variables

-1x+1/2x-(3/2x+6)=0

We get rid of parentheses

-1x+1/2x-3/2x-6=0

We multiply all the terms by the denominator


-1x*2x-6*2x+1-3=0

We add all the numbers together, and all the variables

-1x*2x-6*2x-2=0

Wy multiply elements

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

a = -2; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·(-2)·(-2)
Δ = 128
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:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{2}}{2*-2}=\frac{12-8\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{2}}{2*-2}=\frac{12+8\sqrt{2}}{-4}
$