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

Solution for 1-(2/6x)=3/12x equation:

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

We move all terms to the left:

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


Domain of the equation: 6x)!=0

x!=0/1

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

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

We get rid of parentheses

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

We calculate fractions


(-24x)/72x^2+(-18x)/72x^2+1=0

We multiply all the terms by the denominator


(-24x)+(-18x)+1*72x^2=0

Wy multiply elements

72x^2+(-24x)+(-18x)=0

We get rid of parentheses

72x^2-24x-18x=0

We add all the numbers together, and all the variables

72x^2-42x=0

a = 72; b = -42; c = 0;
Δ = b2-4ac
Δ = -422-4·72·0
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42}{2*72}=\frac{0}{144}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42}{2*72}=\frac{84}{144}
=7/12
$