2/x-6+3/3x-18=14

Solution for 2/x-6+3/3x-18=14 equation:

2/x-6+3/3x-18=14

We move all terms to the left:

2/x-6+3/3x-18-(14)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2/x+3/3x-38=0

We calculate fractions


6x/3x^2+3x/3x^2-38=0

We multiply all the terms by the denominator


6x+3x-38*3x^2=0

We add all the numbers together, and all the variables

9x-38*3x^2=0

Wy multiply elements

-114x^2+9x=0

a = -114; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-114)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-114}=\frac{-18}{-228}
=3/38
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-114}=\frac{0}{-228}
=0
$