a2-19a-216=0

Solution for a2-19a-216=0 equation:

a2-19a-216=0

We add all the numbers together, and all the variables

a^2-19a-216=0

a = 1; b = -19; c = -216;
Δ = b2-4ac
Δ = -192-4·1·(-216)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-35}{2*1}=\frac{-16}{2}
=-8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+35}{2*1}=\frac{54}{2}
=27
$