0=n^2-3n-27

Solution for 0=n^2-3n-27 equation:

0=n^2-3n-27

We move all terms to the left:

0-(n^2-3n-27)=0

We add all the numbers together, and all the variables

-(n^2-3n-27)=0

We get rid of parentheses

-n^2+3n+27=0

We add all the numbers together, and all the variables

-1n^2+3n+27=0

a = -1; b = 3; c = +27;
Δ = b2-4ac
Δ = 32-4·(-1)·27
Δ = 117
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:

$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{13}}{2*-1}=\frac{-3-3\sqrt{13}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{13}}{2*-1}=\frac{-3+3\sqrt{13}}{-2}
$