X^2-24x-3840=0

Solution for X^2-24x-3840=0 equation:

X^2-24X-3840=0

a = 1; b = -24; c = -3840;
Δ = b2-4ac
Δ = -242-4·1·(-3840)
Δ = 15936
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:

$\sqrt{\Delta}=\sqrt{15936}=\sqrt{64*249}=\sqrt{64}*\sqrt{249}=8\sqrt{249}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{249}}{2*1}=\frac{24-8\sqrt{249}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{249}}{2*1}=\frac{24+8\sqrt{249}}{2}
$