16/3x+16=4x

Solution for 16/3x+16=4x equation:

16/3x+16=4x

We move all terms to the left:

16/3x+16-(4x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+16/3x+16=0

We multiply all the terms by the denominator


-4x*3x+16*3x+16=0

Wy multiply elements

-12x^2+48x+16=0

a = -12; b = 48; c = +16;
Δ = b2-4ac
Δ = 482-4·(-12)·16
Δ = 3072
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3072}=\sqrt{1024*3}=\sqrt{1024}*\sqrt{3}=32\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-32\sqrt{3}}{2*-12}=\frac{-48-32\sqrt{3}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+32\sqrt{3}}{2*-12}=\frac{-48+32\sqrt{3}}{-24}
$