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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


36x^2/144x^2+36x/144x^2+240x/144x^2-4-2=0

We add all the numbers together, and all the variables

36x^2/144x^2+36x/144x^2+240x/144x^2-6=0

We multiply all the terms by the denominator


36x^2+36x+240x-6*144x^2=0

We add all the numbers together, and all the variables

36x^2+276x-6*144x^2=0

Wy multiply elements

36x^2-864x^2+276x=0

We add all the numbers together, and all the variables

-828x^2+276x=0

a = -828; b = 276; c = 0;
Δ = b2-4ac
Δ = 2762-4·(-828)·0
Δ = 76176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{76176}=276$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(276)-276}{2*-828}=\frac{-552}{-1656}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(276)+276}{2*-828}=\frac{0}{-1656}
=0
$