F(x)=-3x^2+2x^2+1

Solution for F(x)=-3x^2+2x^2+1 equation:

(F)=-3F^2+2F^2+1

We move all terms to the left:

(F)-(-3F^2+2F^2+1)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

F^2+F-1=0

a = 1; b = 1; c = -1;
Δ = b2-4ac
Δ = 12-4·1·(-1)
Δ = 5
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{5}}{2*1}=\frac{-1-\sqrt{5}}{2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{5}}{2*1}=\frac{-1+\sqrt{5}}{2}
$