n(45-3n)=0

Solution for n(45-3n)=0 equation:

n(45-3n)=0

We add all the numbers together, and all the variables

n(-3n+45)=0

We multiply parentheses

-3n^2+45n=0

a = -3; b = 45; c = 0;
Δ = b2-4ac
Δ = 452-4·(-3)·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-45}{2*-3}=\frac{-90}{-6}
=+15
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+45}{2*-3}=\frac{0}{-6}
=0
$