5.5=-16t^2+45t-3

Solution for 5.5=-16t^2+45t-3 equation:

5.5=-16t^2+45t-3

We move all terms to the left:

5.5-(-16t^2+45t-3)=0

We get rid of parentheses

16t^2-45t+3+5.5=0

We add all the numbers together, and all the variables

16t^2-45t+8.5=0

a = 16; b = -45; c = +8.5;
Δ = b2-4ac
Δ = -452-4·16·8.5
Δ = 1481
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{-(-45)-\sqrt{1481}}{2*16}=\frac{45-\sqrt{1481}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1481}}{2*16}=\frac{45+\sqrt{1481}}{32}
$