0=-5t^2+5t+60

Solution for 0=-5t^2+5t+60 equation:

0=-5t^2+5t+60

We move all terms to the left:

0-(-5t^2+5t+60)=0

We add all the numbers together, and all the variables

-(-5t^2+5t+60)=0

We get rid of parentheses

5t^2-5t-60=0

a = 5; b = -5; c = -60;
Δ = b2-4ac
Δ = -52-4·5·(-60)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-35}{2*5}=\frac{-30}{10}
=-3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+35}{2*5}=\frac{40}{10}
=4
$