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

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

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

We multiply parentheses ..

(+5n^2+4n-5n-4)=0

We get rid of parentheses

5n^2+4n-5n-4=0

We add all the numbers together, and all the variables

5n^2-1n-4=0

a = 5; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·5·(-4)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-9}{2*5}=\frac{-8}{10}
=-4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+9}{2*5}=\frac{10}{10}
=1
$