0=50t-5t^2+30

Solution for 0=50t-5t^2+30 equation:

0=50t-5t^2+30

We move all terms to the left:

0-(50t-5t^2+30)=0

We add all the numbers together, and all the variables

-(50t-5t^2+30)=0

We get rid of parentheses

5t^2-50t-30=0

a = 5; b = -50; c = -30;
Δ = b2-4ac
Δ = -502-4·5·(-30)
Δ = 3100
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:

$\sqrt{\Delta}=\sqrt{3100}=\sqrt{100*31}=\sqrt{100}*\sqrt{31}=10\sqrt{31}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{31}}{2*5}=\frac{50-10\sqrt{31}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{31}}{2*5}=\frac{50+10\sqrt{31}}{10}
$