8x-18=5/(x)

Solution for 8x-18=5/(x) equation:

8x-18=5/(x)

We move all terms to the left:

8x-18-(5/(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

8x-(+5/x)-18=0

We get rid of parentheses

8x-5/x-18=0

We multiply all the terms by the denominator


8x*x-18*x-5=0

We add all the numbers together, and all the variables

-18x+8x*x-5=0

Wy multiply elements

8x^2-18x-5=0

a = 8; b = -18; c = -5;
Δ = b2-4ac
Δ = -182-4·8·(-5)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-22}{2*8}=\frac{-4}{16}
=-1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+22}{2*8}=\frac{40}{16}
=2+1/2
$