(n+5)(5n+2)=0

Solution for (n+5)(5n+2)=0 equation:

(n+5)(5n+2)=0

We multiply parentheses ..

(+5n^2+2n+25n+10)=0

We get rid of parentheses

5n^2+2n+25n+10=0

We add all the numbers together, and all the variables

5n^2+27n+10=0

a = 5; b = 27; c = +10;
Δ = b2-4ac
Δ = 272-4·5·10
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-23}{2*5}=\frac{-50}{10}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+23}{2*5}=\frac{-4}{10}
=-2/5
$