16x+1=64/4x

Solution for 16x+1=64/4x equation:

16x+1=64/4x

We move all terms to the left:

16x+1-(64/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

16x-(+64/4x)+1=0

We get rid of parentheses

16x-64/4x+1=0

We multiply all the terms by the denominator


16x*4x+1*4x-64=0

Wy multiply elements

64x^2+4x-64=0

a = 64; b = 4; c = -64;
Δ = b2-4ac
Δ = 42-4·64·(-64)
Δ = 16400
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:

$\sqrt{\Delta}=\sqrt{16400}=\sqrt{400*41}=\sqrt{400}*\sqrt{41}=20\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-20\sqrt{41}}{2*64}=\frac{-4-20\sqrt{41}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+20\sqrt{41}}{2*64}=\frac{-4+20\sqrt{41}}{128}
$