(3x+6)=(1/2x+12)

Solution for (3x+6)=(1/2x+12) equation:

(3x+6)=(1/2x+12)

We move all terms to the left:

(3x+6)-((1/2x+12))=0


Domain of the equation: 2x+12))!=0

x∈R


We get rid of parentheses

3x-((1/2x+12))+6=0

We multiply all the terms by the denominator


3x*2x+6*2x+12))-((1+12))=0

We add all the numbers together, and all the variables

3x*2x+6*2x+12))-(13)=0

We add all the numbers together, and all the variables

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

Wy multiply elements

6x^2+12x=0

a = 6; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·6·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*6}=\frac{0}{12}
=0
$