(5)/(x)-(1)/(2)=(3)/(6x)

Solution for (5)/(x)-(1)/(2)=(3)/(6x) equation:

(5)/(x)-(1)/(2)=(3)/(6x)

We move all terms to the left:

(5)/(x)-(1)/(2)-((3)/(6x))=0


Domain of the equation: 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

5/x-(+3/6x)-1/2=0

We get rid of parentheses

5/x-3/6x-1/2=0

We calculate fractions


(-36x^2)/24x^2+120x/24x^2+(-12x)/24x^2=0

We multiply all the terms by the denominator


(-36x^2)+120x+(-12x)=0

We get rid of parentheses

-36x^2+120x-12x=0

We add all the numbers together, and all the variables

-36x^2+108x=0

a = -36; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·(-36)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*-36}=\frac{-216}{-72}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*-36}=\frac{0}{-72}
=0
$