-k^2-8=10k

Solution for -k^2-8=10k equation:

-k^2-8=10k

We move all terms to the left:

-k^2-8-(10k)=0

We add all the numbers together, and all the variables

-1k^2-10k-8=0

a = -1; b = -10; c = -8;
Δ = b2-4ac
Δ = -102-4·(-1)·(-8)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{17}}{2*-1}=\frac{10-2\sqrt{17}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{17}}{2*-1}=\frac{10+2\sqrt{17}}{-2}
$