3.5=-16t^2+27t+2.5

Solution for 3.5=-16t^2+27t+2.5 equation:

3.5=-16t^2+27t+2.5

We move all terms to the left:

3.5-(-16t^2+27t+2.5)=0

We get rid of parentheses

16t^2-27t-2.5+3.5=0

We add all the numbers together, and all the variables

16t^2-27t+1=0

a = 16; b = -27; c = +1;
Δ = b2-4ac
Δ = -272-4·16·1
Δ = 665
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{-(-27)-\sqrt{665}}{2*16}=\frac{27-\sqrt{665}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{665}}{2*16}=\frac{27+\sqrt{665}}{32}
$