(9+3n)(5-n)=0

Solution for (9+3n)(5-n)=0 equation:

(9+3n)(5-n)=0

We add all the numbers together, and all the variables

(3n+9)(-1n+5)=0

We multiply parentheses ..

(-3n^2+15n-9n+45)=0

We get rid of parentheses

-3n^2+15n-9n+45=0

We add all the numbers together, and all the variables

-3n^2+6n+45=0

a = -3; b = 6; c = +45;
Δ = b2-4ac
Δ = 62-4·(-3)·45
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-24}{2*-3}=\frac{-30}{-6}
=+5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24}{2*-3}=\frac{18}{-6}
=-3
$