F(x)=-3x^2+5x-1

Solution for F(x)=-3x^2+5x-1 equation:

(F)=-3F^2+5F-1

We move all terms to the left:

(F)-(-3F^2+5F-1)=0

We get rid of parentheses

3F^2-5F+F+1=0

We add all the numbers together, and all the variables

3F^2-4F+1=0

a = 3; b = -4; c = +1;
Δ = b2-4ac
Δ = -42-4·3·1
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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