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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3F^2+3F-8=0

a = 3; b = 3; c = -8;
Δ = b2-4ac
Δ = 32-4·3·(-8)
Δ = 105
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{-(3)-\sqrt{105}}{2*3}=\frac{-3-\sqrt{105}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{105}}{2*3}=\frac{-3+\sqrt{105}}{6}
$