1/6x+12=1/3x-8

Solution for 1/6x+12=1/3x-8 equation:

1/6x+12=1/3x-8

We move all terms to the left:

1/6x+12-(1/3x-8)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x-8)!=0

x∈R


We get rid of parentheses

1/6x-1/3x+8+12=0

We calculate fractions


3x/18x^2+(-6x)/18x^2+8+12=0

We add all the numbers together, and all the variables

3x/18x^2+(-6x)/18x^2+20=0

We multiply all the terms by the denominator


3x+(-6x)+20*18x^2=0

Wy multiply elements

360x^2+3x+(-6x)=0

We get rid of parentheses

360x^2+3x-6x=0

We add all the numbers together, and all the variables

360x^2-3x=0

a = 360; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·360·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*360}=\frac{0}{720}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*360}=\frac{6}{720}
=1/120
$