-3n(n+7)=-33-n

Solution for -3n(n+7)=-33-n equation:

-3n(n+7)=-33-n

We move all terms to the left:

-3n(n+7)-(-33-n)=0

We add all the numbers together, and all the variables

-3n(n+7)-(-1n-33)=0

We multiply parentheses

-3n^2-21n-(-1n-33)=0

We get rid of parentheses

-3n^2-21n+1n+33=0

We add all the numbers together, and all the variables

-3n^2-20n+33=0

a = -3; b = -20; c = +33;
Δ = b2-4ac
Δ = -202-4·(-3)·33
Δ = 796
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{796}=\sqrt{4*199}=\sqrt{4}*\sqrt{199}=2\sqrt{199}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{199}}{2*-3}=\frac{20-2\sqrt{199}}{-6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{199}}{2*-3}=\frac{20+2\sqrt{199}}{-6}
$