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

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

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

We move all terms to the left:

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


Domain of the equation: 2-x))!=0

We move all terms containing x to the left, all other terms to the right

-x))!=-2

x!=-2/1

x!=-2

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

3x*2))-(-2(-1x+15))=0

We add all the numbers together, and all the variables

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

Wy multiply elements

6x^2-1x=0

a = 6; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·6·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*6}=\frac{2}{12}
=1/6
$