x+1/x=2.9

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Solution for x+1/x=2.9 equation:



x+1/x=2.9
We move all terms to the left:
x+1/x-(2.9)=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
x+1/x-2.9=0
We multiply all the terms by the denominator
x*x-(2.9)*x+1=0
We multiply parentheses
x*x-2.9x+1=0
Wy multiply elements
x^2-2.9x+1=0
a = 1; b = -2.9; c = +1;
Δ = b2-4ac
Δ = -2.92-4·1·1
Δ = 4.41
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{-(-2.9)-\sqrt{4.41}}{2*1}=\frac{2.9-\sqrt{4.41}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.9)+\sqrt{4.41}}{2*1}=\frac{2.9+\sqrt{4.41}}{2} $

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