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

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Solution for 1/4(x)-5=1/3(x) equation:



1/4(x)-5=1/3(x)
We move all terms to the left:
1/4(x)-5-(1/3(x))=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 3x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
1/4x-(+1/3x)-5=0
We get rid of parentheses
1/4x-1/3x-5=0
We calculate fractions
3x/12x^2+(-4x)/12x^2-5=0
We multiply all the terms by the denominator
3x+(-4x)-5*12x^2=0
Wy multiply elements
-60x^2+3x+(-4x)=0
We get rid of parentheses
-60x^2+3x-4x=0
We add all the numbers together, and all the variables
-60x^2-1x=0
a = -60; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·(-60)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*-60}=\frac{0}{-120} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*-60}=\frac{2}{-120} =-1/60 $

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