s^2-24s-840=0

Solution for s^2-24s-840=0 equation:

s^2-24s-840=0

a = 1; b = -24; c = -840;
Δ = b2-4ac
Δ = -242-4·1·(-840)
Δ = 3936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3936}=\sqrt{16*246}=\sqrt{16}*\sqrt{246}=4\sqrt{246}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{246}}{2*1}=\frac{24-4\sqrt{246}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{246}}{2*1}=\frac{24+4\sqrt{246}}{2}
$