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

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

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

We move all terms to the left:

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


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-30x^2+36x+1=0

a = -30; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·(-30)·1
Δ = 1416
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:

$\sqrt{\Delta}=\sqrt{1416}=\sqrt{4*354}=\sqrt{4}*\sqrt{354}=2\sqrt{354}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{354}}{2*-30}=\frac{-36-2\sqrt{354}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{354}}{2*-30}=\frac{-36+2\sqrt{354}}{-60}
$