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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3F^2+F+2=0

a = -3; b = 1; c = +2;
Δ = b2-4ac
Δ = 12-4·(-3)·2
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5}{2*-3}=\frac{-6}{-6}
=1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5}{2*-3}=\frac{4}{-6}
=-2/3
$