x+4/x=64

Solution for x+4/x=64 equation:

x+4/x=64

We move all terms to the left:

x+4/x-(64)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-64*x+4=0

We add all the numbers together, and all the variables

-64x+x*x+4=0

Wy multiply elements

x^2-64x+4=0

a = 1; b = -64; c = +4;
Δ = b2-4ac
Δ = -642-4·1·4
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*1}=\frac{64-4\sqrt{255}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{255}}{2*1}=\frac{64+4\sqrt{255}}{2}
$