-50=20t-1/2*9.8t^2

Solution for -50=20t-1/2*9.8t^2 equation:

-50=20t-1/2*9.8t^2

We move all terms to the left:

-50-(20t-1/2*9.8t^2)=0


Domain of the equation: 2*9.8t^2)!=0

t!=0/1

t!=0

t∈R


We get rid of parentheses

-20t+1/2*9.8t^2-50=0

We multiply all the terms by the denominator


-20t*2*9.8t^2-50*2*9.8t^2+1=0

Wy multiply elements

-360t^2*9-900t*9+1=0

Wy multiply elements

-3240t^2-8100t+1=0

a = -3240; b = -8100; c = +1;
Δ = b2-4ac
Δ = -81002-4·(-3240)·1
Δ = 65622960
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:

$\sqrt{\Delta}=\sqrt{65622960}=\sqrt{1296*50635}=\sqrt{1296}*\sqrt{50635}=36\sqrt{50635}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8100)-36\sqrt{50635}}{2*-3240}=\frac{8100-36\sqrt{50635}}{-6480}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8100)+36\sqrt{50635}}{2*-3240}=\frac{8100+36\sqrt{50635}}{-6480}
$