x+1/x=6.8

Solution for x+1/x=6.8 equation:

x+1/x=6.8

We move all terms to the left:

x+1/x-(6.8)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x+1/x-6.8=0

We multiply all the terms by the denominator


x*x-(6.8)*x+1=0

We multiply parentheses

x*x-6.8x+1=0

Wy multiply elements

x^2-6.8x+1=0

a = 1; b = -6.8; c = +1;
Δ = b2-4ac
Δ = -6.82-4·1·1
Δ = 42.24
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{-(-6.8)-\sqrt{42.24}}{2*1}=\frac{6.8-\sqrt{42.24}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6.8)+\sqrt{42.24}}{2*1}=\frac{6.8+\sqrt{42.24}}{2}
$