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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3F^2-1F-3=0

a = 3; b = -1; c = -3;
Δ = b2-4ac
Δ = -12-4·3·(-3)
Δ = 37
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{37}}{2*3}=\frac{1-\sqrt{37}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{37}}{2*3}=\frac{1+\sqrt{37}}{6}
$