6/x-3-1/6x-18=13

Solution for 6/x-3-1/6x-18=13 equation:

6/x-3-1/6x-18=13

We move all terms to the left:

6/x-3-1/6x-18-(13)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

6/x-1/6x-34=0

We calculate fractions


36x/6x^2+(-x)/6x^2-34=0

We add all the numbers together, and all the variables

36x/6x^2+(-1x)/6x^2-34=0

We multiply all the terms by the denominator


36x+(-1x)-34*6x^2=0

Wy multiply elements

-204x^2+36x+(-1x)=0

We get rid of parentheses

-204x^2+36x-1x=0

We add all the numbers together, and all the variables

-204x^2+35x=0

a = -204; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·(-204)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*-204}=\frac{-70}{-408}
=35/204
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*-204}=\frac{0}{-408}
=0
$