x+1/x=45

Solution for x+1/x=45 equation:

x+1/x=45

We move all terms to the left:

x+1/x-(45)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-45*x+1=0

We add all the numbers together, and all the variables

-45x+x*x+1=0

Wy multiply elements

x^2-45x+1=0

a = 1; b = -45; c = +1;
Δ = b2-4ac
Δ = -452-4·1·1
Δ = 2021
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{-(-45)-\sqrt{2021}}{2*1}=\frac{45-\sqrt{2021}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2021}}{2*1}=\frac{45+\sqrt{2021}}{2}
$