2.5=8t-5t^2

Solution for 2.5=8t-5t^2 equation:

2.5=8t-5t^2

We move all terms to the left:

2.5-(8t-5t^2)=0

We get rid of parentheses

5t^2-8t+2.5=0

a = 5; b = -8; c = +2.5;
Δ = b2-4ac
Δ = -82-4·5·2.5
Δ = 14
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{-(-8)-\sqrt{14}}{2*5}=\frac{8-\sqrt{14}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+\sqrt{14}}{2*5}=\frac{8+\sqrt{14}}{10}
$