x+1/x=63

Solution for x+1/x=63 equation:

x+1/x=63

We move all terms to the left:

x+1/x-(63)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-63*x+1=0

We add all the numbers together, and all the variables

-63x+x*x+1=0

Wy multiply elements

x^2-63x+1=0

a = 1; b = -63; c = +1;
Δ = b2-4ac
Δ = -632-4·1·1
Δ = 3965
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{-(-63)-\sqrt{3965}}{2*1}=\frac{63-\sqrt{3965}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+\sqrt{3965}}{2*1}=\frac{63+\sqrt{3965}}{2}
$