20580=1/2(100)v^2

Solution for 20580=1/2(100)v^2 equation:

20580=1/2(100)v^2

We move all terms to the left:

20580-(1/2(100)v^2)=0


Domain of the equation: 2100v^2)!=0

v!=0/1

v!=0

v∈R


We get rid of parentheses

-1/2100v^2+20580=0

We multiply all the terms by the denominator


20580*2100v^2-1=0

Wy multiply elements

43218000v^2-1=0

a = 43218000; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·43218000·(-1)
Δ = 172872000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{172872000}=\sqrt{34574400*5}=\sqrt{34574400}*\sqrt{5}=5880\sqrt{5}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-5880\sqrt{5}}{2*43218000}=\frac{0-5880\sqrt{5}}{86436000}
=-\frac{5880\sqrt{5}}{86436000}
=-\frac{\sqrt{5}}{14700}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+5880\sqrt{5}}{2*43218000}=\frac{0+5880\sqrt{5}}{86436000}
=\frac{5880\sqrt{5}}{86436000}
=\frac{\sqrt{5}}{14700}
$