52=1.9t+9.8t^2/2

Solution for 52=1.9t+9.8t^2/2 equation:

52=1.9t+9.8t^2/2

We move all terms to the left:

52-(1.9t+9.8t^2/2)=0

We get rid of parentheses

-9.8t^2/2-1.9t+52=0

We multiply all the terms by the denominator


-9.8t^2-(1.9t)*2+52*2=0

We add all the numbers together, and all the variables

-9.8t^2-(+1.9t)*2+52*2=0

We add all the numbers together, and all the variables

-9.8t^2-(+1.9t)*2+104=0

We multiply parentheses

-9.8t^2-2t+104=0

a = -9.8; b = -2; c = +104;
Δ = b2-4ac
Δ = -22-4·(-9.8)·104
Δ = 4080.8
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{-(-2)-\sqrt{4080.8}}{2*-9.8}=\frac{2-\sqrt{4080.8}}{-19.6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{4080.8}}{2*-9.8}=\frac{2+\sqrt{4080.8}}{-19.6}
$