3/x+6x+9=0

Solution for 3/x+6x+9=0 equation:

3/x+6x+9=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

6x+3/x+9=0

We multiply all the terms by the denominator


6x*x+9*x+3=0

We add all the numbers together, and all the variables

9x+6x*x+3=0

Wy multiply elements

6x^2+9x+3=0

a = 6; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·6·3
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{-(9)-3}{2*6}=\frac{-12}{12}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3}{2*6}=\frac{-6}{12}
=-1/2
$