x+1/4x=16

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

x+1/4x=16

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-64x+1=0

a = 4; b = -64; c = +1;
Δ = b2-4ac
Δ = -642-4·4·1
Δ = 4080
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:

$\sqrt{\Delta}=\sqrt{4080}=\sqrt{16*255}=\sqrt{16}*\sqrt{255}=4\sqrt{255}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{255}}{2*4}=\frac{64-4\sqrt{255}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{255}}{2*4}=\frac{64+4\sqrt{255}}{8}
$