x/3x+2x=12-x

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



x/3x+2x=12-x
We move all terms to the left:
x/3x+2x-(12-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
x/3x+2x-(-1x+12)=0
We add all the numbers together, and all the variables
2x+x/3x-(-1x+12)=0
We get rid of parentheses
2x+x/3x+1x-12=0
We multiply all the terms by the denominator
2x*3x+x+1x*3x-12*3x=0
We add all the numbers together, and all the variables
x+2x*3x+1x*3x-12*3x=0
Wy multiply elements
6x^2+3x^2+x-36x=0
We add all the numbers together, and all the variables
9x^2-35x=0
a = 9; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·9·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*9}=\frac{0}{18} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*9}=\frac{70}{18} =3+8/9 $

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