F(x)=144-16x^2

Solution for F(x)=144-16x^2 equation:

(F)=144-16F^2

We move all terms to the left:

(F)-(144-16F^2)=0

We get rid of parentheses

16F^2+F-144=0

a = 16; b = 1; c = -144;
Δ = b2-4ac
Δ = 12-4·16·(-144)
Δ = 9217
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{9217}}{2*16}=\frac{-1-\sqrt{9217}}{32}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{9217}}{2*16}=\frac{-1+\sqrt{9217}}{32}
$