200=9.8x^2/2

Solution for 200=9.8x^2/2 equation:

200=9.8x^2/2

We move all terms to the left:

200-(9.8x^2/2)=0

We get rid of parentheses

-9.8x^2/2+200=0

We multiply all the terms by the denominator


-9.8x^2+200*2=0

We add all the numbers together, and all the variables

-9.8x^2+400=0

a = -9.8; b = 0; c = +400;
Δ = b2-4ac
Δ = 02-4·(-9.8)·400
Δ = 15680
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15680}=\sqrt{64*245}=\sqrt{64}*\sqrt{245}=8\sqrt{245}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{245}}{2*-9.8}=\frac{0-8\sqrt{245}}{-19.6}
=-\frac{8\sqrt{245}}{-19.6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{245}}{2*-9.8}=\frac{0+8\sqrt{245}}{-19.6}
=\frac{8\sqrt{245}}{-19.6}
$