221=x+4/x

Solution for 221=x+4/x equation:

221=x+4/x

We move all terms to the left:

221-(x+4/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x+4/x)+221=0

We get rid of parentheses

-x-4/x+221=0

We multiply all the terms by the denominator


-x*x+221*x-4=0

We add all the numbers together, and all the variables

221x-x*x-4=0

Wy multiply elements

-1x^2+221x-4=0

a = -1; b = 221; c = -4;
Δ = b2-4ac
Δ = 2212-4·(-1)·(-4)
Δ = 48825
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:

$\sqrt{\Delta}=\sqrt{48825}=\sqrt{225*217}=\sqrt{225}*\sqrt{217}=15\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(221)-15\sqrt{217}}{2*-1}=\frac{-221-15\sqrt{217}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(221)+15\sqrt{217}}{2*-1}=\frac{-221+15\sqrt{217}}{-2}
$