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

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

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

We multiply parentheses ..

(+5s^2-10s+4s-8)=0

We get rid of parentheses

5s^2-10s+4s-8=0

We add all the numbers together, and all the variables

5s^2-6s-8=0

a = 5; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·5·(-8)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14}{2*5}=\frac{-8}{10}
=-4/5
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14}{2*5}=\frac{20}{10}
=2
$