16/3x=16+14/x+16

Solution for 16/3x=16+14/x+16 equation:

16/3x=16+14/x+16

We move all terms to the left:

16/3x-(16+14/x+16)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: x+16)!=0

x∈R


We add all the numbers together, and all the variables

16/3x-(14/x+32)=0

We get rid of parentheses

16/3x-14/x-32=0

We calculate fractions


16x/3x^2+(-42x)/3x^2-32=0

We multiply all the terms by the denominator


16x+(-42x)-32*3x^2=0

Wy multiply elements

-96x^2+16x+(-42x)=0

We get rid of parentheses

-96x^2+16x-42x=0

We add all the numbers together, and all the variables

-96x^2-26x=0

a = -96; b = -26; c = 0;
Δ = b2-4ac
Δ = -262-4·(-96)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-26}{2*-96}=\frac{0}{-192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+26}{2*-96}=\frac{52}{-192}
=-13/48
$