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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3F^2-1F-11=0

a = 3; b = -1; c = -11;
Δ = b2-4ac
Δ = -12-4·3·(-11)
Δ = 133
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{133}}{2*3}=\frac{1-\sqrt{133}}{6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{133}}{2*3}=\frac{1+\sqrt{133}}{6}
$