30=30+19t-t^2

Solution for 30=30+19t-t^2 equation:

30=30+19t-t^2

We move all terms to the left:

30-(30+19t-t^2)=0

We get rid of parentheses

t^2-19t-30+30=0

We add all the numbers together, and all the variables

t^2-19t=0

a = 1; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·1·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*1}=\frac{0}{2}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*1}=\frac{38}{2}
=19
$