F(x+3)=3x2+4x-2

Solution for F(x+3)=3x2+4x-2 equation:

(F+3)=3F^2+4F-2

We move all terms to the left:

(F+3)-(3F^2+4F-2)=0

We get rid of parentheses

-3F^2+F-4F+3+2=0

We add all the numbers together, and all the variables

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

a = -3; b = -3; c = +5;
Δ = b2-4ac
Δ = -32-4·(-3)·5
Δ = 69
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{-(-3)-\sqrt{69}}{2*-3}=\frac{3-\sqrt{69}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{69}}{2*-3}=\frac{3+\sqrt{69}}{-6}
$