-a^2-18a-20=0

Solution for -a^2-18a-20=0 equation:

-a^2-18a-20=0

We add all the numbers together, and all the variables

-1a^2-18a-20=0

a = -1; b = -18; c = -20;
Δ = b2-4ac
Δ = -182-4·(-1)·(-20)
Δ = 244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{61}}{2*-1}=\frac{18-2\sqrt{61}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{61}}{2*-1}=\frac{18+2\sqrt{61}}{-2}
$