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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

F^2+3F-15=0

a = 1; b = 3; c = -15;
Δ = b2-4ac
Δ = 32-4·1·(-15)
Δ = 69
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{-(3)-\sqrt{69}}{2*1}=\frac{-3-\sqrt{69}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{69}}{2*1}=\frac{-3+\sqrt{69}}{2}
$