k=3+15/k

Solution for k=3+15/k equation:

k=3+15/k

We move all terms to the left:

k-(3+15/k)=0


Domain of the equation: k)!=0

k!=0/1

k!=0

k∈R


We add all the numbers together, and all the variables

k-(15/k+3)=0

We get rid of parentheses

k-15/k-3=0

We multiply all the terms by the denominator


k*k-3*k-15=0

We add all the numbers together, and all the variables

-3k+k*k-15=0

Wy multiply elements

k^2-3k-15=0

a = 1; b = -3; c = -15;
Δ = b2-4ac
Δ = -32-4·1·(-15)
Δ = 69
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{69}}{2*1}=\frac{3-\sqrt{69}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{69}}{2*1}=\frac{3+\sqrt{69}}{2}
$