(5n+4)(8n+5)=0

Solution for (5n+4)(8n+5)=0 equation:

(5n+4)(8n+5)=0

We multiply parentheses ..

(+40n^2+25n+32n+20)=0

We get rid of parentheses

40n^2+25n+32n+20=0

We add all the numbers together, and all the variables

40n^2+57n+20=0

a = 40; b = 57; c = +20;
Δ = b2-4ac
Δ = 572-4·40·20
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-7}{2*40}=\frac{-64}{80}
=-4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+7}{2*40}=\frac{-50}{80}
=-5/8
$