0=60t^2+120t-100

Solution for 0=60t^2+120t-100 equation:

0=60t^2+120t-100

We move all terms to the left:

0-(60t^2+120t-100)=0

We add all the numbers together, and all the variables

-(60t^2+120t-100)=0

We get rid of parentheses

-60t^2-120t+100=0

a = -60; b = -120; c = +100;
Δ = b2-4ac
Δ = -1202-4·(-60)·100
Δ = 38400
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:

$\sqrt{\Delta}=\sqrt{38400}=\sqrt{6400*6}=\sqrt{6400}*\sqrt{6}=80\sqrt{6}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-80\sqrt{6}}{2*-60}=\frac{120-80\sqrt{6}}{-120}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+80\sqrt{6}}{2*-60}=\frac{120+80\sqrt{6}}{-120}
$