18/x-1=3x

Solution for 18/x-1=3x equation:

18/x-1=3x

We move all terms to the left:

18/x-1-(3x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-3x+18/x-1=0

We multiply all the terms by the denominator


-3x*x-1*x+18=0

We add all the numbers together, and all the variables

-1x-3x*x+18=0

Wy multiply elements

-3x^2-1x+18=0

a = -3; b = -1; c = +18;
Δ = b2-4ac
Δ = -12-4·(-3)·18
Δ = 217
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{217}}{2*-3}=\frac{1-\sqrt{217}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{217}}{2*-3}=\frac{1+\sqrt{217}}{-6}
$