9000=1/2(20)t^2

Solution for 9000=1/2(20)t^2 equation:

9000=1/2(20)t^2

We move all terms to the left:

9000-(1/2(20)t^2)=0


Domain of the equation: 220t^2)!=0

t!=0/1

t!=0

t∈R


We get rid of parentheses

-1/220t^2+9000=0

We multiply all the terms by the denominator


9000*220t^2-1=0

Wy multiply elements

1980000t^2-1=0

a = 1980000; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·1980000·(-1)
Δ = 7920000
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:

$\sqrt{\Delta}=\sqrt{7920000}=\sqrt{360000*22}=\sqrt{360000}*\sqrt{22}=600\sqrt{22}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-600\sqrt{22}}{2*1980000}=\frac{0-600\sqrt{22}}{3960000}
=-\frac{600\sqrt{22}}{3960000}
=-\frac{\sqrt{22}}{6600}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+600\sqrt{22}}{2*1980000}=\frac{0+600\sqrt{22}}{3960000}
=\frac{600\sqrt{22}}{3960000}
=\frac{\sqrt{22}}{6600}
$