F(x)=-x^2+10x-16

Solution for F(x)=-x^2+10x-16 equation:

(F)=-F^2+10F-16

We move all terms to the left:

(F)-(-F^2+10F-16)=0

We get rid of parentheses

F^2-10F+F+16=0

We add all the numbers together, and all the variables

F^2-9F+16=0

a = 1; b = -9; c = +16;
Δ = b2-4ac
Δ = -92-4·1·16
Δ = 17
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{-(-9)-\sqrt{17}}{2*1}=\frac{9-\sqrt{17}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{17}}{2*1}=\frac{9+\sqrt{17}}{2}
$