X+1/x=5.2

Solution for X+1/x=5.2 equation:

X+1/X=5.2

We move all terms to the left:

X+1/X-(5.2)=0


Domain of the equation: X!=0

X∈R


We add all the numbers together, and all the variables

X+1/X-5.2=0

We multiply all the terms by the denominator


X*X-(5.2)*X+1=0

We multiply parentheses

X*X-5.2X+1=0

Wy multiply elements

X^2-5.2X+1=0

a = 1; b = -5.2; c = +1;
Δ = b2-4ac
Δ = -5.22-4·1·1
Δ = 23.04
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{-(-5.2)-\sqrt{23.04}}{2*1}=\frac{5.2-\sqrt{23.04}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5.2)+\sqrt{23.04}}{2*1}=\frac{5.2+\sqrt{23.04}}{2}
$