(5s-10)(4s+24)=0

Solution for (5s-10)(4s+24)=0 equation:

(5s-10)(4s+24)=0

We multiply parentheses ..

(+20s^2+120s-40s-240)=0

We get rid of parentheses

20s^2+120s-40s-240=0

We add all the numbers together, and all the variables

20s^2+80s-240=0

a = 20; b = 80; c = -240;
Δ = b2-4ac
Δ = 802-4·20·(-240)
Δ = 25600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25600}=160$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-160}{2*20}=\frac{-240}{40}
=-6
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+160}{2*20}=\frac{80}{40}
=2
$