0=-16t^2+80t-61.5

Solution for 0=-16t^2+80t-61.5 equation:

0=-16t^2+80t-61.5

We move all terms to the left:

0-(-16t^2+80t-61.5)=0

We add all the numbers together, and all the variables

-(-16t^2+80t-61.5)=0

We get rid of parentheses

16t^2-80t+61.5=0

a = 16; b = -80; c = +61.5;
Δ = b2-4ac
Δ = -802-4·16·61.5
Δ = 2464
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:

$\sqrt{\Delta}=\sqrt{2464}=\sqrt{16*154}=\sqrt{16}*\sqrt{154}=4\sqrt{154}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{154}}{2*16}=\frac{80-4\sqrt{154}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{154}}{2*16}=\frac{80+4\sqrt{154}}{32}
$