120=60t-5t^2

Solution for 120=60t-5t^2 equation:

120=60t-5t^2

We move all terms to the left:

120-(60t-5t^2)=0

We get rid of parentheses

5t^2-60t+120=0

a = 5; b = -60; c = +120;
Δ = b2-4ac
Δ = -602-4·5·120
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20\sqrt{3}}{2*5}=\frac{60-20\sqrt{3}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20\sqrt{3}}{2*5}=\frac{60+20\sqrt{3}}{10}
$