0=50t+5t^2

Solution for 0=50t+5t^2 equation:

0=50t+5t^2

We move all terms to the left:

0-(50t+5t^2)=0

We add all the numbers together, and all the variables

-(50t+5t^2)=0

We get rid of parentheses

-5t^2-50t=0

a = -5; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·(-5)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*-5}=\frac{0}{-10}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*-5}=\frac{100}{-10}
=-10
$