6x-8=18/x

Solution for 6x-8=18/x equation:

6x-8=18/x

We move all terms to the left:

6x-8-(18/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+18/x)-8=0

We get rid of parentheses

6x-18/x-8=0

We multiply all the terms by the denominator


6x*x-8*x-18=0

We add all the numbers together, and all the variables

-8x+6x*x-18=0

Wy multiply elements

6x^2-8x-18=0

a = 6; b = -8; c = -18;
Δ = b2-4ac
Δ = -82-4·6·(-18)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{31}}{2*6}=\frac{8-4\sqrt{31}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{31}}{2*6}=\frac{8+4\sqrt{31}}{12}
$