1/4x+5/3-4=2-1/12x

Solution for 1/4x+5/3-4=2-1/12x equation:

1/4x+5/3-4=2-1/12x

We move all terms to the left:

1/4x+5/3-4-(2-1/12x)=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

1/4x-(-1/12x+2)-4+5/3=0

We get rid of parentheses

1/4x+1/12x-2-4+5/3=0

We calculate fractions


240x^2/432x^2+108x/432x^2+36x/432x^2-2-4=0

We add all the numbers together, and all the variables

240x^2/432x^2+108x/432x^2+36x/432x^2-6=0

We multiply all the terms by the denominator


240x^2+108x+36x-6*432x^2=0

We add all the numbers together, and all the variables

240x^2+144x-6*432x^2=0

Wy multiply elements

240x^2-2592x^2+144x=0

We add all the numbers together, and all the variables

-2352x^2+144x=0

a = -2352; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-2352)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-2352}=\frac{-288}{-4704}
=3/49
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-2352}=\frac{0}{-4704}
=0
$