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 = 5208
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:

$\sqrt{\Delta}=\sqrt{5208}=\sqrt{4*1302}=\sqrt{4}*\sqrt{1302}=2\sqrt{1302}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1302}}{2*-6}=\frac{72-2\sqrt{1302}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1302}}{2*-6}=\frac{72+2\sqrt{1302}}{-12}
$