x+1/x=192

Solution for x+1/x=192 equation:

x+1/x=192

We move all terms to the left:

x+1/x-(192)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-192*x+1=0

We add all the numbers together, and all the variables

-192x+x*x+1=0

Wy multiply elements

x^2-192x+1=0

a = 1; b = -192; c = +1;
Δ = b2-4ac
Δ = -1922-4·1·1
Δ = 36860
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{36860}=\sqrt{4*9215}=\sqrt{4}*\sqrt{9215}=2\sqrt{9215}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-2\sqrt{9215}}{2*1}=\frac{192-2\sqrt{9215}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+2\sqrt{9215}}{2*1}=\frac{192+2\sqrt{9215}}{2}
$