0=60t^2+120t-50

Solution for 0=60t^2+120t-50 equation:

0=60t^2+120t-50

We move all terms to the left:

0-(60t^2+120t-50)=0

We add all the numbers together, and all the variables

-(60t^2+120t-50)=0

We get rid of parentheses

-60t^2-120t+50=0

a = -60; b = -120; c = +50;
Δ = b2-4ac
Δ = -1202-4·(-60)·50
Δ = 26400
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:

$\sqrt{\Delta}=\sqrt{26400}=\sqrt{400*66}=\sqrt{400}*\sqrt{66}=20\sqrt{66}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-20\sqrt{66}}{2*-60}=\frac{120-20\sqrt{66}}{-120}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+20\sqrt{66}}{2*-60}=\frac{120+20\sqrt{66}}{-120}
$