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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-96x^2)/864x^2+384x^2/864x^2+432x/864x^2+(-216x)/864x^2=0

We multiply all the terms by the denominator


(-96x^2)+384x^2+432x+(-216x)=0

We add all the numbers together, and all the variables

384x^2+(-96x^2)+432x+(-216x)=0

We get rid of parentheses

384x^2-96x^2+432x-216x=0

We add all the numbers together, and all the variables

288x^2+216x=0

a = 288; b = 216; c = 0;
Δ = b2-4ac
Δ = 2162-4·288·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-216}{2*288}=\frac{-432}{576}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+216}{2*288}=\frac{0}{576}
=0
$