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+15)!=0

x∈R


We get rid of parentheses

x-1/x-15=0

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 = 229
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{229}}{2*1}=\frac{15-\sqrt{229}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{229}}{2*1}=\frac{15+\sqrt{229}}{2}
$