4/k-k=8

Solution for 4/k-k=8 equation:

4/k-k=8

We move all terms to the left:

4/k-k-(8)=0


Domain of the equation: k!=0

k∈R


We add all the numbers together, and all the variables

-1k+4/k-8=0

We multiply all the terms by the denominator


-1k*k-8*k+4=0

We add all the numbers together, and all the variables

-8k-1k*k+4=0

Wy multiply elements

-1k^2-8k+4=0

a = -1; b = -8; c = +4;
Δ = b2-4ac
Δ = -82-4·(-1)·4
Δ = 80
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{80}=\sqrt{16*5}=\sqrt{16}*\sqrt{5}=4\sqrt{5}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{5}}{2*-1}=\frac{8-4\sqrt{5}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{5}}{2*-1}=\frac{8+4\sqrt{5}}{-2}
$