58850=1/2(100)v^2

Solution for 58850=1/2(100)v^2 equation:

58850=1/2(100)v^2

We move all terms to the left:

58850-(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+58850=0

We multiply all the terms by the denominator


58850*2100v^2-1=0

Wy multiply elements

123585000v^2-1=0

a = 123585000; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·123585000·(-1)
Δ = 494340000
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:

$\sqrt{\Delta}=\sqrt{494340000}=\sqrt{10000*49434}=\sqrt{10000}*\sqrt{49434}=100\sqrt{49434}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100\sqrt{49434}}{2*123585000}=\frac{0-100\sqrt{49434}}{247170000}
=-\frac{100\sqrt{49434}}{247170000}
=-\frac{\sqrt{49434}}{2471700}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100\sqrt{49434}}{2*123585000}=\frac{0+100\sqrt{49434}}{247170000}
=\frac{100\sqrt{49434}}{247170000}
=\frac{\sqrt{49434}}{2471700}
$