0=3x/x^2+9

Solution for 0=3x/x^2+9 equation:

0=3x/x^2+9

We move all terms to the left:

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


Domain of the equation: x^2+9)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-3x/x^2-9=0

We multiply all the terms by the denominator


-3x-9*x^2=0

We add all the numbers together, and all the variables

-9x^2-3x=0

a = -9; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-9)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-9}=\frac{0}{-18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-9}=\frac{6}{-18}
=-1/3
$