2.5=-16t^2+40t+4

Solution for 2.5=-16t^2+40t+4 equation:

2.5=-16t^2+40t+4

We move all terms to the left:

2.5-(-16t^2+40t+4)=0

We get rid of parentheses

16t^2-40t-4+2.5=0

We add all the numbers together, and all the variables

16t^2-40t-1.5=0

a = 16; b = -40; c = -1.5;
Δ = b2-4ac
Δ = -402-4·16·(-1.5)
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{106}}{2*16}=\frac{40-4\sqrt{106}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{106}}{2*16}=\frac{40+4\sqrt{106}}{32}
$