(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^2-21n+5=0

a = -20; b = -21; c = +5;
Δ = b2-4ac
Δ = -212-4·(-20)·5
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-29}{2*-20}=\frac{-8}{-40}
=1/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+29}{2*-20}=\frac{50}{-40}
=-1+1/4
$