200=9.81t^2/2

Solution for 200=9.81t^2/2 equation:

200=9.81t^2/2

We move all terms to the left:

200-(9.81t^2/2)=0

We get rid of parentheses

-9.81t^2/2+200=0

We multiply all the terms by the denominator


-9.81t^2+200*2=0

We add all the numbers together, and all the variables

-9.81t^2+400=0

a = -9.81; b = 0; c = +400;
Δ = b2-4ac
Δ = 02-4·(-9.81)·400
Δ = 15696
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15696}=\sqrt{144*109}=\sqrt{144}*\sqrt{109}=12\sqrt{109}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{109}}{2*-9.81}=\frac{0-12\sqrt{109}}{-19.62}
=-\frac{12\sqrt{109}}{-19.62}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{109}}{2*-9.81}=\frac{0+12\sqrt{109}}{-19.62}
=\frac{12\sqrt{109}}{-19.62}
$