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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3F^2+F-1=0

a = 3; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·3·(-1)
Δ = 13
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{-(1)-\sqrt{13}}{2*3}=\frac{-1-\sqrt{13}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{13}}{2*3}=\frac{-1+\sqrt{13}}{6}
$