6/(x-9)=8x

Solution for 6/(x-9)=8x equation:

6/(x-9)=8x

We move all terms to the left:

6/(x-9)-(8x)=0


Domain of the equation: (x-9)!=0

We move all terms containing x to the left, all other terms to the right

x!=9

x∈R


We add all the numbers together, and all the variables

-8x+6/(x-9)=0

We multiply all the terms by the denominator


-8x*(x-9)+6=0

We multiply parentheses

-8x^2+72x+6=0

a = -8; b = 72; c = +6;
Δ = b2-4ac
Δ = 722-4·(-8)·6
Δ = 5376
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:

$\sqrt{\Delta}=\sqrt{5376}=\sqrt{256*21}=\sqrt{256}*\sqrt{21}=16\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-16\sqrt{21}}{2*-8}=\frac{-72-16\sqrt{21}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+16\sqrt{21}}{2*-8}=\frac{-72+16\sqrt{21}}{-16}
$