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

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

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

We move all terms to the left:

1/4x-(5/3x-4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


3x/12x^2+(-20x)/12x^2+4=0

We multiply all the terms by the denominator


3x+(-20x)+4*12x^2=0

Wy multiply elements

48x^2+3x+(-20x)=0

We get rid of parentheses

48x^2+3x-20x=0

We add all the numbers together, and all the variables

48x^2-17x=0

a = 48; b = -17; c = 0;
Δ = b2-4ac
Δ = -172-4·48·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-17}{2*48}=\frac{0}{96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+17}{2*48}=\frac{34}{96}
=17/48
$