F(x)=-16x^2+12x

Solution for F(x)=-16x^2+12x equation:

(F)=-16F^2+12F

We move all terms to the left:

(F)-(-16F^2+12F)=0

We get rid of parentheses

16F^2-12F+F=0

We add all the numbers together, and all the variables

16F^2-11F=0

a = 16; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·16·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*16}=\frac{0}{32}
=0
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*16}=\frac{22}{32}
=11/16
$