F(-2)=-3x^2+9x-8

Solution for F(-2)=-3x^2+9x-8 equation:

(-2)=-3F^2+9F-8

We move all terms to the left:

(-2)-(-3F^2+9F-8)=0

We add all the numbers together, and all the variables

-(-3F^2+9F-8)-2=0

We get rid of parentheses

3F^2-9F+8-2=0

We add all the numbers together, and all the variables

3F^2-9F+6=0

a = 3; b = -9; c = +6;
Δ = b2-4ac
Δ = -92-4·3·6
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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