a^2-19a-400=0

Solution for a^2-19a-400=0 equation:

a^2-19a-400=0

a = 1; b = -19; c = -400;
Δ = b2-4ac
Δ = -192-4·1·(-400)
Δ = 1961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{1961}}{2*1}=\frac{19-\sqrt{1961}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{1961}}{2*1}=\frac{19+\sqrt{1961}}{2}
$