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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3F^2+11F-2=0

a = 3; b = 11; c = -2;
Δ = b2-4ac
Δ = 112-4·3·(-2)
Δ = 145
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{-(11)-\sqrt{145}}{2*3}=\frac{-11-\sqrt{145}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{145}}{2*3}=\frac{-11+\sqrt{145}}{6}
$