5/x-3/12=9/3x

Solution for 5/x-3/12=9/3x equation:

5/x-3/12=9/3x

We move all terms to the left:

5/x-3/12-(9/3x)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/x-(+9/3x)-3/12=0

We get rid of parentheses

5/x-9/3x-3/12=0

We calculate fractions


(-27x^2)/36x^2+180x/36x^2+(-108x)/36x^2=0

We multiply all the terms by the denominator


(-27x^2)+180x+(-108x)=0

We get rid of parentheses

-27x^2+180x-108x=0

We add all the numbers together, and all the variables

-27x^2+72x=0

a = -27; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·(-27)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*-27}=\frac{-144}{-54}
=2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*-27}=\frac{0}{-54}
=0
$