F(n)=n^2+10n

Solution for F(n)=n^2+10n equation:

(F)=F^2+10F

We move all terms to the left:

(F)-(F^2+10F)=0

We get rid of parentheses

-F^2+F-10F=0

We add all the numbers together, and all the variables

-1F^2-9F=0

a = -1; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-1)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-1}=\frac{0}{-2}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-1}=\frac{18}{-2}
=-9
$