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1/4x-6=1/3x

We move all terms to the left:

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

Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R

Domain of the equation: 3x)!=0We add all the numbers together, and all the variables

x!=0/1

x!=0

x∈R

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

We get rid of parentheses

1/4x-1/3x-6=0

We calculate fractions

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

We multiply all the terms by the denominator

3x+(-4x)-6*12x^2=0

Wy multiply elements

-72x^2+3x+(-4x)=0

We get rid of parentheses

-72x^2+3x-4x=0

We add all the numbers together, and all the variables

-72x^2-1x=0

a = -72; b = -1; c = 0;

Δ = b^{2}-4ac

Δ = -1^{2}-4·(-72)·0

Δ = 1

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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-72}=\frac{0}{-144} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-72}=\frac{2}{-144} =-1/72 $

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