F(x)=-16x^2+54x+6

Solution for F(x)=-16x^2+54x+6 equation:

(F)=-16F^2+54F+6

We move all terms to the left:

(F)-(-16F^2+54F+6)=0

We get rid of parentheses

16F^2-54F+F-6=0

We add all the numbers together, and all the variables

16F^2-53F-6=0

a = 16; b = -53; c = -6;
Δ = b2-4ac
Δ = -532-4·16·(-6)
Δ = 3193
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{-(-53)-\sqrt{3193}}{2*16}=\frac{53-\sqrt{3193}}{32}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{3193}}{2*16}=\frac{53+\sqrt{3193}}{32}
$