x^2-8x-1440=0

Solution for x^2-8x-1440=0 equation:

x^2-8x-1440=0

a = 1; b = -8; c = -1440;
Δ = b2-4ac
Δ = -82-4·1·(-1440)
Δ = 5824
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:

$\sqrt{\Delta}=\sqrt{5824}=\sqrt{64*91}=\sqrt{64}*\sqrt{91}=8\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{91}}{2*1}=\frac{8-8\sqrt{91}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{91}}{2*1}=\frac{8+8\sqrt{91}}{2}
$