3/x-6=9x

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

3/x-6=9x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-9x+3/x-6=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -9; b = -6; c = +3;
Δ = b2-4ac
Δ = -62-4·(-9)·3
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*-9}=\frac{-6}{-18}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12}{2*-9}=\frac{18}{-18}
=-1
$