1/3x=2x+12

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

1/3x=2x+12

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/3x-2x-12=0

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -6; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·(-6)·1
Δ = 1320
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:

$\sqrt{\Delta}=\sqrt{1320}=\sqrt{4*330}=\sqrt{4}*\sqrt{330}=2\sqrt{330}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-2\sqrt{330}}{2*-6}=\frac{36-2\sqrt{330}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+2\sqrt{330}}{2*-6}=\frac{36+2\sqrt{330}}{-12}
$