-5s^2-24s-10=0

Solution for -5s^2-24s-10=0 equation:

-5s^2-24s-10=0

a = -5; b = -24; c = -10;
Δ = b2-4ac
Δ = -242-4·(-5)·(-10)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{94}}{2*-5}=\frac{24-2\sqrt{94}}{-10}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{94}}{2*-5}=\frac{24+2\sqrt{94}}{-10}
$