F(-2)=3x2-5

Solution for F(-2)=3x2-5 equation:

(-2)=3F^2-5

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-3F^2+5-2=0

We add all the numbers together, and all the variables

-3F^2+3=0

a = -3; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-3)·3
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6}{2*-3}=\frac{-6}{-6}
=1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6}{2*-3}=\frac{6}{-6}
=-1
$