1/3x+9-2/x+3=2

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Solution for 1/3x+9-2/x+3=2 equation: 



1/3x+9-2/x+3=2

We move all terms to the left:

1/3x+9-2/x+3-(2)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R





Domain of the equation: x!=0

x∈R



We add all the numbers together, and all the variables

1/3x-2/x+10=0

We calculate fractions


x/3x^2+(-6x)/3x^2+10=0

We multiply all the terms by the denominator


x+(-6x)+10*3x^2=0

Wy multiply elements

30x^2+x+(-6x)=0

We get rid of parentheses

30x^2+x-6x=0

We add all the numbers together, and all the variables

30x^2-5x=0

a = 30; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·30·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*30}=\frac{0}{60}
=0
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*30}=\frac{10}{60}
=1/6
$

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