0=60t^2+120t-60

Solution for 0=60t^2+120t-60 equation:

0=60t^2+120t-60

We move all terms to the left:

0-(60t^2+120t-60)=0

We add all the numbers together, and all the variables

-(60t^2+120t-60)=0

We get rid of parentheses

-60t^2-120t+60=0

a = -60; b = -120; c = +60;
Δ = b2-4ac
Δ = -1202-4·(-60)·60
Δ = 28800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{28800}=\sqrt{14400*2}=\sqrt{14400}*\sqrt{2}=120\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-120\sqrt{2}}{2*-60}=\frac{120-120\sqrt{2}}{-120}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+120\sqrt{2}}{2*-60}=\frac{120+120\sqrt{2}}{-120}
$