0=-6t^2+30t

Solution for 0=-6t^2+30t equation:

0=-6t^2+30t

We move all terms to the left:

0-(-6t^2+30t)=0

We add all the numbers together, and all the variables

-(-6t^2+30t)=0

We get rid of parentheses

6t^2-30t=0

a = 6; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·6·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*6}=\frac{0}{12}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*6}=\frac{60}{12}
=5
$