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

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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 $

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