x+1/x=15

Solution for x+1/x=15 equation:

x+1/x=15

We move all terms to the left:

x+1/x-(15)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-15*x+1=0

We add all the numbers together, and all the variables

-15x+x*x+1=0

Wy multiply elements

x^2-15x+1=0

a = 1; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·1·1
Δ = 221
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{-(-15)-\sqrt{221}}{2*1}=\frac{15-\sqrt{221}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{221}}{2*1}=\frac{15+\sqrt{221}}{2}
$