2x-4+4=18/x

Solution for 2x-4+4=18/x equation:

2x-4+4=18/x

We move all terms to the left:

2x-4+4-(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

2x-(+18/x)-4+4=0

We add all the numbers together, and all the variables

2x-(+18/x)=0

We get rid of parentheses

2x-18/x=0

We multiply all the terms by the denominator


2x*x-18=0

Wy multiply elements

2x^2-18=0

a = 2; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·2·(-18)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*2}=\frac{12}{4}
=3
$