x^2-40x-384=0.

Solution for x^2-40x-384=0. equation:

x^2-40x-384=0.

a = 1; b = -40; c = -384;
Δ = b2-4ac
Δ = -402-4·1·(-384)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-56}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+56}{2*1}=\frac{96}{2}
=48
$