n=n^2-6n-3

Solution for n=n^2-6n-3 equation:

n=n^2-6n-3

We move all terms to the left:

n-(n^2-6n-3)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1n^2+7n+3=0

a = -1; b = 7; c = +3;
Δ = b2-4ac
Δ = 72-4·(-1)·3
Δ = 61
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{-(7)-\sqrt{61}}{2*-1}=\frac{-7-\sqrt{61}}{-2}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{61}}{2*-1}=\frac{-7+\sqrt{61}}{-2}
$