F(x)=0.05x2+9.5x-200

Solution for F(x)=0.05x2+9.5x-200 equation:

(F)=0.05F^2+9.5F-200

We move all terms to the left:

(F)-(0.05F^2+9.5F-200)=0

We get rid of parentheses

-0.05F^2+F-9.5F+200=0

We add all the numbers together, and all the variables

-0.05F^2-8.5F+200=0

a = -0.05; b = -8.5; c = +200;
Δ = b2-4ac
Δ = -8.52-4·(-0.05)·200
Δ = 112.25
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{-(-8.5)-\sqrt{112.25}}{2*-0.05}=\frac{8.5-\sqrt{112.25}}{-0.1}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8.5)+\sqrt{112.25}}{2*-0.05}=\frac{8.5+\sqrt{112.25}}{-0.1}
$