x^2-24x-105=0

Solution for x^2-24x-105=0 equation:

x^2-24x-105=0

a = 1; b = -24; c = -105;
Δ = b2-4ac
Δ = -242-4·1·(-105)
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{249}}{2*1}=\frac{24-2\sqrt{249}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{249}}{2*1}=\frac{24+2\sqrt{249}}{2}
$