50=2.1t+9.8t^2/2

Solution for 50=2.1t+9.8t^2/2 equation:

50=2.1t+9.8t^2/2

We move all terms to the left:

50-(2.1t+9.8t^2/2)=0

We get rid of parentheses

-9.8t^2/2-2.1t+50=0

We multiply all the terms by the denominator


-9.8t^2-(2.1t)*2+50*2=0

We add all the numbers together, and all the variables

-9.8t^2-(+2.1t)*2+50*2=0

We add all the numbers together, and all the variables

-9.8t^2-(+2.1t)*2+100=0

We multiply parentheses

-9.8t^2-4t+100=0

a = -9.8; b = -4; c = +100;
Δ = b2-4ac
Δ = -42-4·(-9.8)·100
Δ = 3936
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:

$\sqrt{\Delta}=\sqrt{3936}=\sqrt{16*246}=\sqrt{16}*\sqrt{246}=4\sqrt{246}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{246}}{2*-9.8}=\frac{4-4\sqrt{246}}{-19.6}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{246}}{2*-9.8}=\frac{4+4\sqrt{246}}{-19.6}
$