F(x)=-6x^2+12x+21

Solution for F(x)=-6x^2+12x+21 equation:

(F)=-6F^2+12F+21

We move all terms to the left:

(F)-(-6F^2+12F+21)=0

We get rid of parentheses

6F^2-12F+F-21=0

We add all the numbers together, and all the variables

6F^2-11F-21=0

a = 6; b = -11; c = -21;
Δ = b2-4ac
Δ = -112-4·6·(-21)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-25}{2*6}=\frac{-14}{12}
=-1+1/6
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+25}{2*6}=\frac{36}{12}
=3
$