x/3x+2x=20

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Solution for x/3x+2x=20 equation:



x/3x+2x=20
We move all terms to the left:
x/3x+2x-(20)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We add all the numbers together, and all the variables
2x+x/3x-20=0
We multiply all the terms by the denominator
2x*3x+x-20*3x=0
We add all the numbers together, and all the variables
x+2x*3x-20*3x=0
Wy multiply elements
6x^2+x-60x=0
We add all the numbers together, and all the variables
6x^2-59x=0
a = 6; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·6·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*6}=\frac{0}{12} =0 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*6}=\frac{118}{12} =9+5/6 $

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