9/x+6=3x

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

9/x+6=3x

We move all terms to the left:

9/x+6-(3x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-3x+9/x+6=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

6x-3x*x+9=0

Wy multiply elements

-3x^2+6x+9=0

a = -3; b = 6; c = +9;
Δ = b2-4ac
Δ = 62-4·(-3)·9
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*-3}=\frac{6}{-6}
=-1
$