x+1/x=2.225

Solution for x+1/x=2.225 equation:

x+1/x=2.225

We move all terms to the left:

x+1/x-(2.225)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+1/x-2.225=0

We multiply all the terms by the denominator


x*x-(2.225)*x+1=0

We multiply parentheses

x*x-2.225x+1=0

Wy multiply elements

x^2-2.225x+1=0

a = 1; b = -2.225; c = +1;
Δ = b2-4ac
Δ = -2.2252-4·1·1
Δ = 0.950625
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{-(-2.225)-\sqrt{0.950625}}{2*1}=\frac{2.225-\sqrt{0.950625}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.225)+\sqrt{0.950625}}{2*1}=\frac{2.225+\sqrt{0.950625}}{2}
$