9/x-6=4x

Solution for 9/x-6=4x equation:

9/x-6=4x

We move all terms to the left:

9/x-6-(4x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-4x+9/x-6=0

We multiply all the terms by the denominator


-4x*x-6*x+9=0

We add all the numbers together, and all the variables

-6x-4x*x+9=0

Wy multiply elements

-4x^2-6x+9=0

a = -4; b = -6; c = +9;
Δ = b2-4ac
Δ = -62-4·(-4)·9
Δ = 180
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{5}}{2*-4}=\frac{6-6\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{5}}{2*-4}=\frac{6+6\sqrt{5}}{-8}
$