F(x)=16x-0.1x^2-100

Solution for F(x)=16x-0.1x^2-100 equation:

(F)=16F-0.1F^2-100

We move all terms to the left:

(F)-(16F-0.1F^2-100)=0

We get rid of parentheses

0.1F^2-16F+F+100=0

We add all the numbers together, and all the variables

0.1F^2-15F+100=0

a = 0.1; b = -15; c = +100;
Δ = b2-4ac
Δ = -152-4·0.1·100
Δ = 185
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{-(-15)-\sqrt{185}}{2*0.1}=\frac{15-\sqrt{185}}{0.2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{185}}{2*0.1}=\frac{15+\sqrt{185}}{0.2}
$