X+1/x=20

Solution for X+1/x=20 equation:

X+1/X=20

We move all terms to the left:

X+1/X-(20)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-20*X+1=0

We add all the numbers together, and all the variables

-20X+X*X+1=0

Wy multiply elements

X^2-20X+1=0

a = 1; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·1·1
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{11}}{2*1}=\frac{20-6\sqrt{11}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{11}}{2*1}=\frac{20+6\sqrt{11}}{2}
$