-17=12t-5t2

Solution for -17=12t-5t2 equation:

-17=12t-5t^2

We move all terms to the left:

-17-(12t-5t^2)=0

We get rid of parentheses

5t^2-12t-17=0

a = 5; b = -12; c = -17;
Δ = b2-4ac
Δ = -122-4·5·(-17)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-22}{2*5}=\frac{-10}{10}
=-1
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+22}{2*5}=\frac{34}{10}
=3+2/5
$