F(x)=-16x^2+48x+100

Solution for F(x)=-16x^2+48x+100 equation:

(F)=-16F^2+48F+100

We move all terms to the left:

(F)-(-16F^2+48F+100)=0

We get rid of parentheses

16F^2-48F+F-100=0

We add all the numbers together, and all the variables

16F^2-47F-100=0

a = 16; b = -47; c = -100;
Δ = b2-4ac
Δ = -472-4·16·(-100)
Δ = 8609
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{-(-47)-\sqrt{8609}}{2*16}=\frac{47-\sqrt{8609}}{32}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{8609}}{2*16}=\frac{47+\sqrt{8609}}{32}
$