F(x)=-2x^2-8x+18

Solution for F(x)=-2x^2-8x+18 equation:

(F)=-2F^2-8F+18

We move all terms to the left:

(F)-(-2F^2-8F+18)=0

We get rid of parentheses

2F^2+8F+F-18=0

We add all the numbers together, and all the variables

2F^2+9F-18=0

a = 2; b = 9; c = -18;
Δ = b2-4ac
Δ = 92-4·2·(-18)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-15}{2*2}=\frac{-24}{4}
=-6
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+15}{2*2}=\frac{6}{4}
=1+1/2
$