F(0)=-3x^2-11x+4

Solution for F(0)=-3x^2-11x+4 equation:

(0)=-3F^2-11F+4

We move all terms to the left:

(0)-(-3F^2-11F+4)=0

We add all the numbers together, and all the variables

-(-3F^2-11F+4)=0

We get rid of parentheses

3F^2+11F-4=0

a = 3; b = 11; c = -4;
Δ = b2-4ac
Δ = 112-4·3·(-4)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-13}{2*3}=\frac{-24}{6}
=-4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+13}{2*3}=\frac{2}{6}
=1/3
$