F(x)=-3x2-x+2

Solution for F(x)=-3x2-x+2 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3F^2+2F-2=0

a = 3; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·3·(-2)
Δ = 28
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{7}}{2*3}=\frac{-2-2\sqrt{7}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{7}}{2*3}=\frac{-2+2\sqrt{7}}{6}
$