17=29.5t-5t^2

Solution for 17=29.5t-5t^2 equation:

17=29.5t-5t^2

We move all terms to the left:

17-(29.5t-5t^2)=0

We get rid of parentheses

5t^2-29.5t+17=0

a = 5; b = -29.5; c = +17;
Δ = b2-4ac
Δ = -29.52-4·5·17
Δ = 530.25
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{-(-29.5)-\sqrt{530.25}}{2*5}=\frac{29.5-\sqrt{530.25}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29.5)+\sqrt{530.25}}{2*5}=\frac{29.5+\sqrt{530.25}}{10}
$