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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3F^2-1F+2=0

a = -3; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-3)·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*-3}=\frac{-4}{-6}
=2/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*-3}=\frac{6}{-6}
=-1
$