1/4x=1/3x-8

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Solution for 1/4x=1/3x-8 equation:



1/4x=1/3x-8
We move all terms to the left:
1/4x-(1/3x-8)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 3x-8)!=0
x∈R
We get rid of parentheses
1/4x-1/3x+8=0
We calculate fractions
3x/12x^2+(-4x)/12x^2+8=0
We multiply all the terms by the denominator
3x+(-4x)+8*12x^2=0
Wy multiply elements
96x^2+3x+(-4x)=0
We get rid of parentheses
96x^2+3x-4x=0
We add all the numbers together, and all the variables
96x^2-1x=0
a = 96; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·96·0
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*96}=\frac{0}{192} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*96}=\frac{2}{192} =1/96 $

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