F(x)=-0.4x^2+9x+1

Solution for F(x)=-0.4x^2+9x+1 equation:

(F)=-0.4F^2+9F+1

We move all terms to the left:

(F)-(-0.4F^2+9F+1)=0

We get rid of parentheses

0.4F^2-9F+F-1=0

We add all the numbers together, and all the variables

0.4F^2-8F-1=0

a = 0.4; b = -8; c = -1;
Δ = b2-4ac
Δ = -82-4·0.4·(-1)
Δ = 65.6
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)-\sqrt{65.6}}{2*0.4}=\frac{8-\sqrt{65.6}}{0.8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+\sqrt{65.6}}{2*0.4}=\frac{8+\sqrt{65.6}}{0.8}
$