F(t)=-16t^2+32t+5.2

Solution for F(t)=-16t^2+32t+5.2 equation:

(F)=-16F^2+32F+5.2

We move all terms to the left:

(F)-(-16F^2+32F+5.2)=0

We get rid of parentheses

16F^2-32F+F-5.2=0

We add all the numbers together, and all the variables

16F^2-31F-5.2=0

a = 16; b = -31; c = -5.2;
Δ = b2-4ac
Δ = -312-4·16·(-5.2)
Δ = 1293.8
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{-(-31)-\sqrt{1293.8}}{2*16}=\frac{31-\sqrt{1293.8}}{32}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1293.8}}{2*16}=\frac{31+\sqrt{1293.8}}{32}
$