0.5=30t-5t^2

Solution for 0.5=30t-5t^2 equation:

0.5=30t-5t^2

We move all terms to the left:

0.5-(30t-5t^2)=0

We get rid of parentheses

5t^2-30t+0.5=0

a = 5; b = -30; c = +0.5;
Δ = b2-4ac
Δ = -302-4·5·0.5
Δ = 890
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{-(-30)-\sqrt{890}}{2*5}=\frac{30-\sqrt{890}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+\sqrt{890}}{2*5}=\frac{30+\sqrt{890}}{10}
$