2/x-8=9x

Solution for 2/x-8=9x equation:

2/x-8=9x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-9x+2/x-8=0

We multiply all the terms by the denominator


-9x*x-8*x+2=0

We add all the numbers together, and all the variables

-8x-9x*x+2=0

Wy multiply elements

-9x^2-8x+2=0

a = -9; b = -8; c = +2;
Δ = b2-4ac
Δ = -82-4·(-9)·2
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{34}}{2*-9}=\frac{8-2\sqrt{34}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{34}}{2*-9}=\frac{8+2\sqrt{34}}{-18}
$