-4x+18=18/x

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

-4x+18=18/x

We move all terms to the left:

-4x+18-(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

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

We get rid of parentheses

-4x-18/x+18=0

We multiply all the terms by the denominator


-4x*x+18*x-18=0

We add all the numbers together, and all the variables

18x-4x*x-18=0

Wy multiply elements

-4x^2+18x-18=0

a = -4; b = 18; c = -18;
Δ = b2-4ac
Δ = 182-4·(-4)·(-18)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6}{2*-4}=\frac{-12}{-8}
=1+1/2
$