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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


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

We calculate fractions


(-36x^2)/576x^2+192x/576x^2+48x/576x^2-3=0

We multiply all the terms by the denominator


(-36x^2)+192x+48x-3*576x^2=0

We add all the numbers together, and all the variables

(-36x^2)+240x-3*576x^2=0

Wy multiply elements

(-36x^2)-1728x^2+240x=0

We get rid of parentheses

-36x^2-1728x^2+240x=0

We add all the numbers together, and all the variables

-1764x^2+240x=0

a = -1764; b = 240; c = 0;
Δ = b2-4ac
Δ = 2402-4·(-1764)·0
Δ = 57600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{57600}=240$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-240}{2*-1764}=\frac{-480}{-3528}
=20/147
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+240}{2*-1764}=\frac{0}{-3528}
=0
$