F(x+2)=3x^2+2x-5

Solution for F(x+2)=3x^2+2x-5 equation:

(F+2)=3F^2+2F-5

We move all terms to the left:

(F+2)-(3F^2+2F-5)=0

We get rid of parentheses

-3F^2+F-2F+2+5=0

We add all the numbers together, and all the variables

-3F^2-1F+7=0

a = -3; b = -1; c = +7;
Δ = b2-4ac
Δ = -12-4·(-3)·7
Δ = 85
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{85}}{2*-3}=\frac{1-\sqrt{85}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{85}}{2*-3}=\frac{1+\sqrt{85}}{-6}
$