3/x+16=1/3x

Solution for 3/x+16=1/3x equation:

3/x+16=1/3x

We move all terms to the left:

3/x+16-(1/3x)=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

3/x-(+1/3x)+16=0

We get rid of parentheses

3/x-1/3x+16=0

We calculate fractions


9x/3x^2+(-x)/3x^2+16=0

We add all the numbers together, and all the variables

9x/3x^2+(-1x)/3x^2+16=0

We multiply all the terms by the denominator


9x+(-1x)+16*3x^2=0

Wy multiply elements

48x^2+9x+(-1x)=0

We get rid of parentheses

48x^2+9x-1x=0

We add all the numbers together, and all the variables

48x^2+8x=0

a = 48; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·48·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*48}=\frac{-16}{96}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*48}=\frac{0}{96}
=0
$