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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3F^2+9F-2=0

a = 3; b = 9; c = -2;
Δ = b2-4ac
Δ = 92-4·3·(-2)
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{-(9)-\sqrt{105}}{2*3}=\frac{-9-\sqrt{105}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{105}}{2*3}=\frac{-9+\sqrt{105}}{6}
$