K=n2+9n+1

Solution for K=n2+9n+1 equation:

=K2+9K+1

We move all terms to the left:

-(K2+9K+1)=0

We add all the numbers together, and all the variables

-(+K^2+9K+1)=0

We get rid of parentheses

-K^2-9K-1=0

We add all the numbers together, and all the variables

-1K^2-9K-1=0

a = -1; b = -9; c = -1;
Δ = b2-4ac
Δ = -92-4·(-1)·(-1)
Δ = 77
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$K_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{77}}{2*-1}=\frac{9-\sqrt{77}}{-2}
$
$K_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{77}}{2*-1}=\frac{9+\sqrt{77}}{-2}
$