2x+1/x=21

Solution for 2x+1/x=21 equation:

2x+1/x=21

We move all terms to the left:

2x+1/x-(21)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-21*x+1=0

We add all the numbers together, and all the variables

-21x+2x*x+1=0

Wy multiply elements

2x^2-21x+1=0

a = 2; b = -21; c = +1;
Δ = b2-4ac
Δ = -212-4·2·1
Δ = 433
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{433}}{2*2}=\frac{21-\sqrt{433}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{433}}{2*2}=\frac{21+\sqrt{433}}{4}
$