X+2x+1/x=66

Solution for X+2x+1/x=66 equation:

X+2X+1/X=66

We move all terms to the left:

X+2X+1/X-(66)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

3X+1/X-66=0

We multiply all the terms by the denominator


3X*X-66*X+1=0

We add all the numbers together, and all the variables

-66X+3X*X+1=0

Wy multiply elements

3X^2-66X+1=0

a = 3; b = -66; c = +1;
Δ = b2-4ac
Δ = -662-4·3·1
Δ = 4344
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:

$\sqrt{\Delta}=\sqrt{4344}=\sqrt{4*1086}=\sqrt{4}*\sqrt{1086}=2\sqrt{1086}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1086}}{2*3}=\frac{66-2\sqrt{1086}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1086}}{2*3}=\frac{66+2\sqrt{1086}}{6}
$