F(x)=15+2x-x^2

Solution for F(x)=15+2x-x^2 equation:

(F)=15+2F-F^2

We move all terms to the left:

(F)-(15+2F-F^2)=0

We get rid of parentheses

F^2-2F+F-15=0

We add all the numbers together, and all the variables

F^2-1F-15=0

a = 1; b = -1; c = -15;
Δ = b2-4ac
Δ = -12-4·1·(-15)
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{61}}{2*1}=\frac{1-\sqrt{61}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{61}}{2*1}=\frac{1+\sqrt{61}}{2}
$