15/k=k+3

Solution for 15/k=k+3 equation:

15/k=k+3

We move all terms to the left:

15/k-(k+3)=0


Domain of the equation: k!=0

k∈R


We get rid of parentheses

15/k-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

-1k^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}
$