-1/3x-5+1/6x-11=12

Solution for -1/3x-5+1/6x-11=12 equation:

-1/3x-5+1/6x-11=12

We move all terms to the left:

-1/3x-5+1/6x-11-(12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

-1/3x+1/6x-28=0

We calculate fractions


(-6x)/18x^2+3x/18x^2-28=0

We multiply all the terms by the denominator


(-6x)+3x-28*18x^2=0

We add all the numbers together, and all the variables

3x+(-6x)-28*18x^2=0

Wy multiply elements

-504x^2+3x+(-6x)=0

We get rid of parentheses

-504x^2+3x-6x=0

We add all the numbers together, and all the variables

-504x^2-3x=0

a = -504; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-504)·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*-504}=\frac{0}{-1008}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-504}=\frac{6}{-1008}
=-1/168
$