22=1/2(600)(v)^2

Solution for 22=1/2(600)(v)^2 equation:

22=1/2(600)(v)^2

We move all terms to the left:

22-(1/2(600)(v)^2)=0


Domain of the equation: 2600v^2)!=0

v!=0/1

v!=0

v∈R


We get rid of parentheses

-1/2600v^2+22=0

We multiply all the terms by the denominator


22*2600v^2-1=0

Wy multiply elements

57200v^2-1=0

a = 57200; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·57200·(-1)
Δ = 228800
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:

$\sqrt{\Delta}=\sqrt{228800}=\sqrt{1600*143}=\sqrt{1600}*\sqrt{143}=40\sqrt{143}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{143}}{2*57200}=\frac{0-40\sqrt{143}}{114400}
=-\frac{40\sqrt{143}}{114400}
=-\frac{\sqrt{143}}{2860}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{143}}{2*57200}=\frac{0+40\sqrt{143}}{114400}
=\frac{40\sqrt{143}}{114400}
=\frac{\sqrt{143}}{2860}
$