52=1.9t+4.9t^2

Solution for 52=1.9t+4.9t^2 equation:

52=1.9t+4.9t^2

We move all terms to the left:

52-(1.9t+4.9t^2)=0

We get rid of parentheses

-4.9t^2-1.9t+52=0

a = -4.9; b = -1.9; c = +52;
Δ = b2-4ac
Δ = -1.92-4·(-4.9)·52
Δ = 1022.81
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{-(-1.9)-\sqrt{1022.81}}{2*-4.9}=\frac{1.9-\sqrt{1022.81}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.9)+\sqrt{1022.81}}{2*-4.9}=\frac{1.9+\sqrt{1022.81}}{-9.8}
$