1/x+1/6x=1/18

Solution for 1/x+1/6x=1/18 equation:

1/x+1/6x=1/18

We move all terms to the left:

1/x+1/6x-(1/18)=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

1/x+1/6x-(+1/18)=0

We get rid of parentheses

1/x+1/6x-1/18=0

We calculate fractions


(-36x^2)/108x^2+108x/108x^2+18x/108x^2=0

We multiply all the terms by the denominator


(-36x^2)+108x+18x=0

We add all the numbers together, and all the variables

(-36x^2)+126x=0

We get rid of parentheses

-36x^2+126x=0

a = -36; b = 126; c = 0;
Δ = b2-4ac
Δ = 1262-4·(-36)·0
Δ = 15876
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15876}=126$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-126}{2*-36}=\frac{-252}{-72}
=3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+126}{2*-36}=\frac{0}{-72}
=0
$