(4n+5)(5n+1)=0

Solution for (4n+5)(5n+1)=0 equation:

(4n+5)(5n+1)=0

We multiply parentheses ..

(+20n^2+4n+25n+5)=0

We get rid of parentheses

20n^2+4n+25n+5=0

We add all the numbers together, and all the variables

20n^2+29n+5=0

a = 20; b = 29; c = +5;
Δ = b2-4ac
Δ = 292-4·20·5
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-21}{2*20}=\frac{-50}{40}
=-1+1/4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+21}{2*20}=\frac{-8}{40}
=-1/5
$