n(11-3n)=-500

Solution for n(11-3n)=-500 equation:

n(11-3n)=-500

We move all terms to the left:

n(11-3n)-(-500)=0

We add all the numbers together, and all the variables

n(-3n+11)-(-500)=0

We add all the numbers together, and all the variables

n(-3n+11)+500=0

We multiply parentheses

-3n^2+11n+500=0

a = -3; b = 11; c = +500;
Δ = b2-4ac
Δ = 112-4·(-3)·500
Δ = 6121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{6121}}{2*-3}=\frac{-11-\sqrt{6121}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{6121}}{2*-3}=\frac{-11+\sqrt{6121}}{-6}
$