1/3x+12=36-2x

Solution for 1/3x+12=36-2x equation:

1/3x+12=36-2x

We move all terms to the left:

1/3x+12-(36-2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-(-2x+36)+12=0

We get rid of parentheses

1/3x+2x-36+12=0

We multiply all the terms by the denominator


2x*3x-36*3x+12*3x+1=0

Wy multiply elements

6x^2-108x+36x+1=0

We add all the numbers together, and all the variables

6x^2-72x+1=0

a = 6; b = -72; c = +1;
Δ = b2-4ac
Δ = -722-4·6·1
Δ = 5160
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:

$\sqrt{\Delta}=\sqrt{5160}=\sqrt{4*1290}=\sqrt{4}*\sqrt{1290}=2\sqrt{1290}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1290}}{2*6}=\frac{72-2\sqrt{1290}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1290}}{2*6}=\frac{72+2\sqrt{1290}}{12}
$