3/x-1/6x-26=13

Solution for 3/x-1/6x-26=13 equation:

3/x-1/6x-26=13

We move all terms to the left:

3/x-1/6x-26-(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

3/x-1/6x-39=0

We calculate fractions


18x/6x^2+(-x)/6x^2-39=0

We add all the numbers together, and all the variables

18x/6x^2+(-1x)/6x^2-39=0

We multiply all the terms by the denominator


18x+(-1x)-39*6x^2=0

Wy multiply elements

-234x^2+18x+(-1x)=0

We get rid of parentheses

-234x^2+18x-1x=0

We add all the numbers together, and all the variables

-234x^2+17x=0

a = -234; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-234)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-234}=\frac{-34}{-468}
=17/234
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-234}=\frac{0}{-468}
=0
$