x^2-80x-384=0

Solution for x^2-80x-384=0 equation:

x^2-80x-384=0

a = 1; b = -80; c = -384;
Δ = b2-4ac
Δ = -802-4·1·(-384)
Δ = 7936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7936}=\sqrt{256*31}=\sqrt{256}*\sqrt{31}=16\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-16\sqrt{31}}{2*1}=\frac{80-16\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+16\sqrt{31}}{2*1}=\frac{80+16\sqrt{31}}{2}
$