8k=k^2+11

Solution for 8k=k^2+11 equation:

8k=k^2+11

We move all terms to the left:

8k-(k^2+11)=0

We get rid of parentheses

-k^2+8k-11=0

We add all the numbers together, and all the variables

-1k^2+8k-11=0

a = -1; b = 8; c = -11;
Δ = b2-4ac
Δ = 82-4·(-1)·(-11)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{5}}{2*-1}=\frac{-8-2\sqrt{5}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{5}}{2*-1}=\frac{-8+2\sqrt{5}}{-2}
$