18.4=19.82t^2-19t

Solution for 18.4=19.82t^2-19t equation:

18.4=19.82t^2-19t

We move all terms to the left:

18.4-(19.82t^2-19t)=0

We get rid of parentheses

-19.82t^2+19t+18.4=0

a = -19.82; b = 19; c = +18.4;
Δ = b2-4ac
Δ = 192-4·(-19.82)·18.4
Δ = 1819.752
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{-(19)-\sqrt{1819.752}}{2*-19.82}=\frac{-19-\sqrt{1819.752}}{-39.64}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{1819.752}}{2*-19.82}=\frac{-19+\sqrt{1819.752}}{-39.64}
$