0=5t+0.05t^2

Solution for 0=5t+0.05t^2 equation:

0=5t+0.05t^2

We move all terms to the left:

0-(5t+0.05t^2)=0

We add all the numbers together, and all the variables

-(5t+0.05t^2)=0

We get rid of parentheses

-0.05t^2-5t=0

a = -0.05; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-0.05)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-0.05}=\frac{0}{-0.1}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-0.05}=\frac{10}{-0.1}
=-100
$