x+1/x=2.05

Solution for x+1/x=2.05 equation:

x+1/x=2.05

We move all terms to the left:

x+1/x-(2.05)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+1/x-2.05=0

We multiply all the terms by the denominator


x*x-(2.05)*x+1=0

We multiply parentheses

x*x-2.05x+1=0

Wy multiply elements

x^2-2.05x+1=0

a = 1; b = -2.05; c = +1;
Δ = b2-4ac
Δ = -2.052-4·1·1
Δ = 0.2025
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{-(-2.05)-\sqrt{0.2025}}{2*1}=\frac{2.05-\sqrt{0.2025}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.05)+\sqrt{0.2025}}{2*1}=\frac{2.05+\sqrt{0.2025}}{2}
$