(5s-2)(4s+9)=0

Solution for (5s-2)(4s+9)=0 equation:

(5s-2)(4s+9)=0

We multiply parentheses ..

(+20s^2+45s-8s-18)=0

We get rid of parentheses

20s^2+45s-8s-18=0

We add all the numbers together, and all the variables

20s^2+37s-18=0

a = 20; b = 37; c = -18;
Δ = b2-4ac
Δ = 372-4·20·(-18)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-53}{2*20}=\frac{-90}{40}
=-2+1/4
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+53}{2*20}=\frac{16}{40}
=2/5
$