F(x)=-2x^2-6x+9

Solution for F(x)=-2x^2-6x+9 equation:

(F)=-2F^2-6F+9

We move all terms to the left:

(F)-(-2F^2-6F+9)=0

We get rid of parentheses

2F^2+6F+F-9=0

We add all the numbers together, and all the variables

2F^2+7F-9=0

a = 2; b = 7; c = -9;
Δ = b2-4ac
Δ = 72-4·2·(-9)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*2}=\frac{-18}{4}
=-4+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*2}=\frac{4}{4}
=1
$