0=5t^2+12t-17

Solution for 0=5t^2+12t-17 equation:

0=5t^2+12t-17

We move all terms to the left:

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

We add all the numbers together, and all the variables

-(5t^2+12t-17)=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
$