3=3t-0.5t^2

Solution for 3=3t-0.5t^2 equation:

3=3t-0.5t^2

We move all terms to the left:

3-(3t-0.5t^2)=0

We get rid of parentheses

0.5t^2-3t+3=0

a = 0.5; b = -3; c = +3;
Δ = b2-4ac
Δ = -32-4·0.5·3
Δ = 3
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{-(-3)-\sqrt{3}}{2*0.5}=\frac{3-\sqrt{3}}{1}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{3}}{2*0.5}=\frac{3+\sqrt{3}}{1}
$