k^2-17=8k

Solution for k^2-17=8k equation:

k^2-17=8k

We move all terms to the left:

k^2-17-(8k)=0

a = 1; b = -8; c = -17;
Δ = b2-4ac
Δ = -82-4·1·(-17)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{33}}{2*1}=\frac{8-2\sqrt{33}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{33}}{2*1}=\frac{8+2\sqrt{33}}{2}
$