0=-5t^2-12t+65

Solution for 0=-5t^2-12t+65 equation:

0=-5t^2-12t+65

We move all terms to the left:

0-(-5t^2-12t+65)=0

We add all the numbers together, and all the variables

-(-5t^2-12t+65)=0

We get rid of parentheses

5t^2+12t-65=0

a = 5; b = 12; c = -65;
Δ = b2-4ac
Δ = 122-4·5·(-65)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-38}{2*5}=\frac{-50}{10}
=-5
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+38}{2*5}=\frac{26}{10}
=2+3/5
$