100-a^2-6a-9=0

Solution for 100-a^2-6a-9=0 equation:

100-a^2-6a-9=0

We add all the numbers together, and all the variables

-1a^2-6a+91=0

a = -1; b = -6; c = +91;
Δ = b2-4ac
Δ = -62-4·(-1)·91
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-20}{2*-1}=\frac{-14}{-2}
=+7
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+20}{2*-1}=\frac{26}{-2}
=-13
$