8/k=2+k

Solution for 8/k=2+k equation:

8/k=2+k

We move all terms to the left:

8/k-(2+k)=0


Domain of the equation: k!=0

k∈R


We add all the numbers together, and all the variables

8/k-(k+2)=0

We get rid of parentheses

8/k-k-2=0

We multiply all the terms by the denominator


-k*k-2*k+8=0

We add all the numbers together, and all the variables

-2k-k*k+8=0

Wy multiply elements

-1k^2-2k+8=0

a = -1; b = -2; c = +8;
Δ = b2-4ac
Δ = -22-4·(-1)·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*-1}=\frac{-4}{-2}
=+2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*-1}=\frac{8}{-2}
=-4
$