4x+16/4x=16

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

4x+16/4x=16

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

16x^2-64x+16=0

a = 16; b = -64; c = +16;
Δ = b2-4ac
Δ = -642-4·16·16
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{-(-64)-32\sqrt{3}}{2*16}=\frac{64-32\sqrt{3}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+32\sqrt{3}}{2*16}=\frac{64+32\sqrt{3}}{32}
$