t=-16t^2+38.4t+18

Solution for t=-16t^2+38.4t+18 equation:

t=-16t^2+38.4t+18

We move all terms to the left:

t-(-16t^2+38.4t+18)=0

We get rid of parentheses

16t^2-38.4t+t-18=0

We add all the numbers together, and all the variables

16t^2-37.4t-18=0

a = 16; b = -37.4; c = -18;
Δ = b2-4ac
Δ = -37.42-4·16·(-18)
Δ = 2550.76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37.4)-\sqrt{2550.76}}{2*16}=\frac{37.4-\sqrt{2550.76}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37.4)+\sqrt{2550.76}}{2*16}=\frac{37.4+\sqrt{2550.76}}{32}
$