1x/3x=x

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Solution for 1x/3x=x equation:



1x/3x=x
We move all terms to the left:
1x/3x-(x)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
-1x+1x/3x=0
We multiply all the terms by the denominator
-1x*3x+1x=0
We add all the numbers together, and all the variables
x-1x*3x=0
Wy multiply elements
-3x^2+x=0
a = -3; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-3)·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*-3}=\frac{-2}{-6} =1/3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-3}=\frac{0}{-6} =0 $

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