-k^2-16k+84=0

Solution for -k^2-16k+84=0 equation:

-k^2-16k+84=0

We add all the numbers together, and all the variables

-1k^2-16k+84=0

a = -1; b = -16; c = +84;
Δ = b2-4ac
Δ = -162-4·(-1)·84
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{37}}{2*-1}=\frac{16-4\sqrt{37}}{-2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{37}}{2*-1}=\frac{16+4\sqrt{37}}{-2}
$