0=-20t^2+450t-300

Solution for 0=-20t^2+450t-300 equation:

0=-20t^2+450t-300

We move all terms to the left:

0-(-20t^2+450t-300)=0

We add all the numbers together, and all the variables

-(-20t^2+450t-300)=0

We get rid of parentheses

20t^2-450t+300=0

a = 20; b = -450; c = +300;
Δ = b2-4ac
Δ = -4502-4·20·300
Δ = 178500
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:

$\sqrt{\Delta}=\sqrt{178500}=\sqrt{100*1785}=\sqrt{100}*\sqrt{1785}=10\sqrt{1785}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-10\sqrt{1785}}{2*20}=\frac{450-10\sqrt{1785}}{40}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+10\sqrt{1785}}{2*20}=\frac{450+10\sqrt{1785}}{40}
$