0=0.6t^2-0.5t

Solution for 0=0.6t^2-0.5t equation:

0=0.6t^2-0.5t

We move all terms to the left:

0-(0.6t^2-0.5t)=0

We add all the numbers together, and all the variables

-(0.6t^2-0.5t)=0

We get rid of parentheses

-0.6t^2+0.5t=0

a = -0.6; b = 0.5; c = 0;
Δ = b2-4ac
Δ = 0.52-4·(-0.6)·0
Δ = 0.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.5)-\sqrt{0.25}}{2*-0.6}=\frac{-0.5-\sqrt{0.25}}{-1.2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.5)+\sqrt{0.25}}{2*-0.6}=\frac{-0.5+\sqrt{0.25}}{-1.2}
$