57=1.9t+9.8t^2/2

Solution for 57=1.9t+9.8t^2/2 equation:

57=1.9t+9.8t^2/2

We move all terms to the left:

57-(1.9t+9.8t^2/2)=0

We get rid of parentheses

-9.8t^2/2-1.9t+57=0

We multiply all the terms by the denominator


-9.8t^2-(1.9t)*2+57*2=0

We add all the numbers together, and all the variables

-9.8t^2-(+1.9t)*2+57*2=0

We add all the numbers together, and all the variables

-9.8t^2-(+1.9t)*2+114=0

We multiply parentheses

-9.8t^2-2t+114=0

a = -9.8; b = -2; c = +114;
Δ = b2-4ac
Δ = -22-4·(-9.8)·114
Δ = 4472.8
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{4472.8}}{2*-9.8}=\frac{2-\sqrt{4472.8}}{-19.6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{4472.8}}{2*-9.8}=\frac{2+\sqrt{4472.8}}{-19.6}
$