X+1/x=3

Solution for X+1/x=3 equation:

X+1/X=3

We move all terms to the left:

X+1/X-(3)=0


Domain of the equation: X!=0

X∈R


We multiply all the terms by the denominator


X*X-3*X+1=0

We add all the numbers together, and all the variables

-3X+X*X+1=0

Wy multiply elements

X^2-3X+1=0

a = 1; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·1·1
Δ = 5
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{-(-3)-\sqrt{5}}{2*1}=\frac{3-\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{5}}{2*1}=\frac{3+\sqrt{5}}{2}
$