t=-16t^2+40t+9

Solution for t=-16t^2+40t+9 equation:

t=-16t^2+40t+9

We move all terms to the left:

t-(-16t^2+40t+9)=0

We get rid of parentheses

16t^2-40t+t-9=0

We add all the numbers together, and all the variables

16t^2-39t-9=0

a = 16; b = -39; c = -9;
Δ = b2-4ac
Δ = -392-4·16·(-9)
Δ = 2097
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2097}=\sqrt{9*233}=\sqrt{9}*\sqrt{233}=3\sqrt{233}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{233}}{2*16}=\frac{39-3\sqrt{233}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{233}}{2*16}=\frac{39+3\sqrt{233}}{32}
$