F(2)=3x^2+2x-6

Solution for F(2)=3x^2+2x-6 equation:

(2)=3F^2+2F-6

We move all terms to the left:

(2)-(3F^2+2F-6)=0

We get rid of parentheses

-3F^2-2F+6+2=0

We add all the numbers together, and all the variables

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

a = -3; b = -2; c = +8;
Δ = b2-4ac
Δ = -22-4·(-3)·8
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*-3}=\frac{-8}{-6}
=1+1/3
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*-3}=\frac{12}{-6}
=-2
$