F(x)=4x+9-2x^2

Solution for F(x)=4x+9-2x^2 equation:

(F)=4F+9-2F^2

We move all terms to the left:

(F)-(4F+9-2F^2)=0

We get rid of parentheses

2F^2-4F+F-9=0

We add all the numbers together, and all the variables

2F^2-3F-9=0

a = 2; b = -3; c = -9;
Δ = b2-4ac
Δ = -32-4·2·(-9)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9}{2*2}=\frac{-6}{4}
=-1+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9}{2*2}=\frac{12}{4}
=3
$