(6/x)+(7/6x)=44

Solution for (6/x)+(7/6x)=44 equation:

(6/x)+(7/6x)=44

We move all terms to the left:

(6/x)+(7/6x)-(44)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+6/x)+(+7/6x)-44=0

We get rid of parentheses

6/x+7/6x-44=0

We calculate fractions


36x/6x^2+7x/6x^2-44=0

We multiply all the terms by the denominator


36x+7x-44*6x^2=0

We add all the numbers together, and all the variables

43x-44*6x^2=0

Wy multiply elements

-264x^2+43x=0

a = -264; b = 43; c = 0;
Δ = b2-4ac
Δ = 432-4·(-264)·0
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-43}{2*-264}=\frac{-86}{-528}
=43/264
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+43}{2*-264}=\frac{0}{-528}
=0
$