3/4x-2=-6+1/12x

Solution for 3/4x-2=-6+1/12x equation:

3/4x-2=-6+1/12x

We move all terms to the left:

3/4x-2-(-6+1/12x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(1/12x-6)-2=0

We get rid of parentheses

3/4x-1/12x+6-2=0

We calculate fractions


36x/48x^2+(-4x)/48x^2+6-2=0

We add all the numbers together, and all the variables

36x/48x^2+(-4x)/48x^2+4=0

We multiply all the terms by the denominator


36x+(-4x)+4*48x^2=0

Wy multiply elements

192x^2+36x+(-4x)=0

We get rid of parentheses

192x^2+36x-4x=0

We add all the numbers together, and all the variables

192x^2+32x=0

a = 192; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·192·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*192}=\frac{-64}{384}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*192}=\frac{0}{384}
=0
$