F(x)=3x2+2x-1

Solution for F(x)=3x2+2x-1 equation:

(F)=3F^2+2F-1

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3F^2-1F+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}
$